Polarized neutron scattering studies of chiral criticality, and new universality classes of phase transitions

NASA Astrophysics Data System (ADS)

Plakhty, V. P.; Wosnitza, J.; Kulda, J.; Brückel, Th.; Schweika, W.; Visser, D.; Gavrilov, S. V.; Moskvin, E. V.; Kremer, R. K.; Banks, M. G.

2006-11-01

Using a novel polarised neutron scattering technique, the critical exponents for the spin chirality and chiral susceptibility are determined for the triangular lattice antiferromagnet (TLA) CsMnBr 3 in the ranges of reduced temperature τ>10 -3 and τ>7×10 -3, respectively. Their values, βC=0.44(2) and γC=0.85(3), together with the scaling relation α+2β+γ=2.13(9), including the critical exponent where α for the specific heat, prove that the spin-ordering transition belongs to the XY chiral universality class. In the case of helimagnet Ho, it is found that β-2β=0.14(4), where β is the staggered magnetisation exponent. The scaling relation α+2β+γ=2 could be fulfilled with a reasonable α=0.23(4), although for the chiral critical exponents βC=0.90(2) and γC=0.69(5) one needs α=-0.49(5) in contradiction with any experimental data. As the scaling relation always holds, we assume that the spin-ordering transition in Ho is of the first order. In the quantum antiferromagnet CsCuCl 3, a triangular spin order coexists with a long-period Dzyaloshinskii helix. The Dzyaloshinskii axial vector should remove the helix chiral degeneracy, which has not been observed in reality. The critical exponent β=0.22(2) is found to be in agreement with the XY chiral scenario for a TLA. Chiral scattering above TN is very weak, probably being masked by zero-point quantum fluctuations. A modulation of the crystal structure with the periodicity of the helix is observed, indicating strong coupling of the Dzyaloshinskii-Moriya interaction with the lattice.

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; de Albuquerque, Douglas F.

1997-02-01

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Testing critical point universality along the λ-line

NASA Astrophysics Data System (ADS)

Nissen, J. A.; Swanson, D. R.; Geng, Z. K.; Dohm, V.; Israelsson, U. E.; DiPirro, M. J.; Lipa, J. A.

1998-02-01

We are currently building a prototype for a new test of critical-point universality at the lambda transition in 4He, which is to be performed in microgravity conditions. The flight experiment will measure the second-sound velocity as a function of temperature at pressures from 1 to 30 bars in the region close to the lambda line. The critical exponents and other parameters characterizing the behavior of the superfluid density will be determined from the measurements. The microgravity measurements will be quite extensive, probably taking 30 days to complete. In addition to the superfluid density, some measurements of the specific heat will be made using the low-g simulator at the Jet Propulsion Laboratory. The results of the superfluid density and specific heat measurements will be used to compare the asymptotic exponents and other universal aspects of the superfluid density with the theoretical predictions currently established by renormalization group techniques.

Critical exponents and universal magnetic behavior of noncentrosymmetric Fe0.6Co0.4Si

NASA Astrophysics Data System (ADS)

Shanmukharao Samatham, S.; Suresh, K. G.

2018-05-01

The critical magnetic properties of a non-centrosymmetric B20 cubic helimagnet Fe0.6Co0.4Si are investigated using magnetization isotherms. It belongs to the 3D-Heisenberg universality class with short range magnetic coupling as inferred from the self-consistent critical exponents , , and in combination with exchange interaction . Itinerant magnetic nature of the compound is realized by the Rhodes–Wholfarth analysis. Field-induced weak first (parahelical) to second (parafield-polarized) order transition is reported to occur at low critical field due to the weak spin–orbit coupling arising from the weak Dzyaloshinksii–Moriya interactions. Our study suggests the distinct phenomenological magnetic structures for Fe-based cubic magnets (Fe1‑x Co x Si and FeGe) and MnSi which cause contrasting physical properties.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

PubMed

Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing

2017-12-01

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N>1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N=1 up to the thermodynamic limit.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing

2017-12-01

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N >1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N =1 up to the thermodynamic limit.

Universality classes for unstable crystal growth

NASA Astrophysics Data System (ADS)

Biagi, Sofia; Misbah, Chaouqi; Politi, Paolo

2014-06-01

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established 2+1-dimensional family of continuum nonlinear equations for the local height h(x,t) of a crystal surface having the general form ∂th(x,t)=-∇.[j(∇h)+∇(∇2h)]: j (∇h) is an arbitrary function, which is linear for small ∇h, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size L and height H. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, n, controlling the increase in time of the typical size of the pattern, L ˜tn; (ii) the exponent β, controlling the increase in time of the typical slope of the pattern, M ˜tβ, where M ≈H/L. Our study reveals that there are only two different universality classes, according to the presence (n =1/3, β =0) or the absence (n =1/4, β >0) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current j (∇h) and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

Equilibrium and nonequilibrium models on Solomon networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2016-05-01

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio γ/ν, β/ν and 1/ν. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

The fourth law of black-hole thermodynamics

NASA Astrophysics Data System (ADS)

Lousto, C. O.

1993-12-01

We show that black holes fulfill the scaling laws arising in critical transitions. In particular, we find that in the transition from negative to positive values the heat capacities CJQ, CΩQ and CJΦ give rise to critical exponents satisfying the scaling laws. The three transitions have the same critical exponents as predicted by the universality hypothesis. We also briefly discuss the implications of this result with regards to the connections among gravitation, quantum mechanics and statistical physics. Permanent address: Instituto de Astronomía y Física del Espacio, Casilla de Correo 67-Sucursal 28, 1428 Buenos Aires, Argentina.

Critical exponents and universal magnetic behavior of noncentrosymmetric Fe0.6Co0.4Si.

PubMed

Samatham, S Shanmukharao; Suresh, K G

2018-05-31

The critical magnetic properties of a non-centrosymmetric B20 cubic helimagnet Fe 0.6 Co 0.4 Si are investigated using magnetization isotherms. It belongs to the 3D-Heisenberg universality class with short range magnetic coupling as inferred from the self-consistent critical exponents [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in combination with exchange interaction [Formula: see text]. Itinerant magnetic nature of the compound is realized by the Rhodes-Wholfarth analysis. Field-induced weak first (para[Formula: see text]helical) to second (para[Formula: see text]field-polarized) order transition is reported to occur at low critical field due to the weak spin-orbit coupling arising from the weak Dzyaloshinksii-Moriya interactions. Our study suggests the distinct phenomenological magnetic structures for Fe-based cubic magnets (Fe 1-x Co x Si and FeGe) and MnSi which cause contrasting physical properties.

Jamming criticality revealed by removing localized buckling excitations.

PubMed

Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Zamponi, Francesco

2015-03-27

Recent theoretical advances offer an exact, first-principles theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badiev, M. K., E-mail: m-zagir@mail.ru; Murtazaev, A. K.; Ramazanov, M. K.

2016-10-15

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scalingmore » theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.« less

Scaling universality at the dynamic vortex Mott transition

DOE PAGES

Lankhorst, M.; Poccia, N.; Stehno, M. P.; ...

2018-01-17

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory formore » the DMT based on the parity reflection-time reversal (PT) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.« less

Scaling universality at the dynamic vortex Mott transition

NASA Astrophysics Data System (ADS)

Lankhorst, M.; Poccia, N.; Stehno, M. P.; Galda, A.; Barman, H.; Coneri, F.; Hilgenkamp, H.; Brinkman, A.; Golubov, A. A.; Tripathi, V.; Baturina, T. I.; Vinokur, V. M.

2018-01-01

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the DMT based on the parity reflection-time reversal (P T ) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.

Scaling analysis of [Fe(pyrazole)4]2[Nb(CN)8] molecular magnet

NASA Astrophysics Data System (ADS)

Konieczny, P.; Pełka, R.; Zieliński, P. M.; Pratt, F. L.; Pinkowicz, D.; Sieklucka, B.; Wasiutyński, T.

2013-10-01

The critical behaviour of the three dimensional (3D) molecular magnet {[FeII(pirazol)4]2[NbIV(CN)8]·4H2O}n has been studied with the use of experimental techniques such as ac magnetometry and zero field μSR spectroscopy. The sample orders magnetically below Tc=7.8 K. The measurements allowed to determine static exponents β, γ, and the dynamic exponent w. The resulting exponent values indicate that the studied system belongs to the universality class of the 3D Heisenberg model.

Collapsing lattice animals and lattice trees in two dimensions

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Grassberger, Peter

2005-06-01

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second-order transitions from an extended to a collapsed phase in the resulting two-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond-driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P* where a transition line between two collapsed phases (one bond driven and the other contact driven) sparks off. This point P* seems to be attractive (in the renormalization group sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.

The nature of the continuous non-equilibrium phase transition of Axelrod's model

NASA Astrophysics Data System (ADS)

Peres, Lucas R.; Fontanari, José F.

2015-09-01

Axelrod's model in the square lattice with nearest-neighbors interactions exhibits culturally homogeneous as well as culturally fragmented absorbing configurations. In the case in which the agents are characterized by F = 2 cultural features and each feature assumes k states drawn from a Poisson distribution of parameter q, these regimes are separated by a continuous transition at qc = 3.10 +/- 0.02 . Using Monte Carlo simulations and finite-size scaling we show that the mean density of cultural domains μ is an order parameter of the model that vanishes as μ ∼ (q - q_c)^β with β = 0.67 +/- 0.01 at the critical point. In addition, for the correlation length critical exponent we find ν = 1.63 +/- 0.04 and for Fisher's exponent, τ = 1.76 +/- 0.01 . This set of critical exponents places the continuous phase transition of Axelrod's model apart from the known universality classes of non-equilibrium lattice models.

Universality class of the two-dimensional polymer collapse transition

NASA Astrophysics Data System (ADS)

Nahum, Adam

2016-05-01

The nature of the θ point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur for an exactly solvable model. We use a representation of the problem via the CPN -1σ model in the limit N →1 to determine the stability of this critical point. First we prove that the Duplantier-Saleur (DS) critical exponents are robust, so long as the polymer does not cross itself: They can arise in a generic lattice model and do not require fine-tuning. This resolves a longstanding theoretical question. We also address an apparent paradox: Two different lattice models, apparently both in the DS universality class, show different numbers of relevant perturbations, apparently leading to contradictory conclusions about the stability of the DS exponents. We explain this in terms of subtle differences between the two models, one of which is fine-tuned (and not strictly in the DS universality class). Next we allow the polymer to cross itself, as appropriate, e.g., to the quasi-two-dimensional case. This introduces an additional independent relevant perturbation, so we do not expect the DS exponents to apply. The exponents in the case with crossings will be those of the generic tricritical O (n ) model at n =0 and different from the case without crossings. We also discuss interesting features of the operator content of the CPN -1 model. Simple geometrical arguments show that two operators in this field theory, with very different symmetry properties, have the same scaling dimension for any value of N (or, equivalently, any value of the loop fugacity). Also we argue that for any value of N the CPN -1 model has a marginal odd-parity operator that is related to the winding angle.

Scaling identity connects human mobility and social interactions.

PubMed

Deville, Pierre; Song, Chaoming; Eagle, Nathan; Blondel, Vincent D; Barabási, Albert-László; Wang, Dashun

2016-06-28

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.

Relation between self-organized criticality and grain aspect ratio in granular piles

NASA Astrophysics Data System (ADS)

Denisov, D. V.; Villanueva, Y. Y.; Lőrincz, K. A.; May, S.; Wijngaarden, R. J.

2012-05-01

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth (β) and roughness (α) exponents, the avalanche fractal dimension (D), the avalanche size distribution exponent (τ), the critical angle (γ), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined τ. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.

Scaling identity connects human mobility and social interactions

PubMed Central

Deville, Pierre; Song, Chaoming; Eagle, Nathan; Blondel, Vincent D.; Barabási, Albert-László; Wang, Dashun

2016-01-01

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality. PMID:27274050

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

PubMed

Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi; Gambassi, Andrea

2015-10-01

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Critical behavior of the van der Waals bonded ferromagnet Fe3 -xGeTe2

NASA Astrophysics Data System (ADS)

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

2017-10-01

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe3 -xGeTe2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe3 -xGeTe2 single crystals grown by self-flux method with Fe deficiency x ≈0.36 exhibit bulk FM ordering below Tc=152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β =0.372 (4 ) with a critical temperature Tc=151.25 (5 ) K and γ =1.265 (15 ) with Tc=151.17 (12 ) K are obtained by the Kouvel-Fisher method, whereas δ =4.50 (1 ) is obtained by a critical isotherm analysis at Tc=151 K. These critical exponents obey the Widom scaling relation δ =1 +γ /β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M (H ) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m =f±(h ) , where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d =3 ,n =3 ) spins coupled with the attractive long-range interactions between spins that decay as J (r ) ≈r-(3 +σ ) with σ =1.89 .

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

NASA Astrophysics Data System (ADS)

Yu, Yi-Cong; Guan, Xi-Wen

2017-06-01

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent ν = 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension. Supported by the National Natural Science Foundation of China under Grant No 11374331 and the key NSFC under Grant No 11534014. XWG has been partially supported by the Australian Research Council.

Susceptibility of the Ising Model on a Kagomé Lattice by Using Wang-Landau Sampling

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon; Kwak, Wooseop

2018-03-01

The susceptibility of the Ising model on a kagomé lattice has never been obtained. We investigate the properties of the kagomé-lattice Ising model by using the Wang-Landau sampling method. We estimate both the magnetic scaling exponent yh = 1.90(1) and the thermal scaling exponent yt = 1.04(2) only from the susceptibility. From the estimated values of yh and yt, we obtain all the critical exponents, the specific-heat critical exponent α = 0.08(4), the spontaneous-magnetization critical exponent β = 0.10(1), the susceptibility critical exponent γ = 1.73(5), the isothermalmagnetization critical exponent δ = 16(4), the correlation-length critical exponent ν = 0.96(2), and the correlation-function critical exponent η = 0.20(4), without using any other thermodynamic function, such as the specific heat, magnetization, correlation length, and correlation function. One should note that the evaluation of all the critical exponents only from information on the susceptibility is an innovative approach.

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Chen, Sheng; Täuber, Uwe C.

2016-04-01

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

NASA Astrophysics Data System (ADS)

Schlief, Andres; Lunts, Peter; Lee, Sung-Sik

2017-04-01

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

Critical behavior of the van der Waals bonded ferromagnet Fe 3 - x GeTe 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe 3-xGeTe 2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe 3-xGeTe 2 single crystals grown by self-flux method with Fe deficiency x ≈ 0.36 exhibit bulk FM ordering below T c = 152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β = 0.372(4) with a critical temperature T c= 151.25(5) K and γ = 1.265(15) with T c = 151.17(12) K are obtained by the Kouvel-Fisher method,more » whereas δ = 4.50 ( 1 ) is obtained by a critical isotherm analysis at T c = 151 K. These critical exponents obey the Widom scaling relation δ = 1 + γ / β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M(H) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m = f±(h), where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d = 3,n = 3) spins coupled with the attractive long-range interactions between spins that decay as J(r) ≈ r -(3+σ) with σ = 1.89.« less

Critical behavior of the van der Waals bonded ferromagnet Fe 3 - x GeTe 2

DOE PAGES

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

2017-10-29

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe 3-xGeTe 2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe 3-xGeTe 2 single crystals grown by self-flux method with Fe deficiency x ≈ 0.36 exhibit bulk FM ordering below T c = 152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β = 0.372(4) with a critical temperature T c= 151.25(5) K and γ = 1.265(15) with T c = 151.17(12) K are obtained by the Kouvel-Fisher method,more » whereas δ = 4.50 ( 1 ) is obtained by a critical isotherm analysis at T c = 151 K. These critical exponents obey the Widom scaling relation δ = 1 + γ / β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M(H) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m = f±(h), where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d = 3,n = 3) spins coupled with the attractive long-range interactions between spins that decay as J(r) ≈ r -(3+σ) with σ = 1.89.« less

Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction

NASA Astrophysics Data System (ADS)

He, Peng; Jiang, Yuzhu; Guan, Xiwen; He, Jinyu

2015-01-01

Quantum criticality of strongly attractive Fermi gas with SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations. The phase transitions driven by the chemical potential μ , effective magnetic field H1, H2 (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the TBA equations in the zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2 and correlation length exponent ν =1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multicomponent Fermi gases with SU(N) symmetry.

Critical field-exponents for secure message-passing in modular networks

NASA Astrophysics Data System (ADS)

Shekhtman, Louis M.; Danziger, Michael M.; Bonamassa, Ivan; Buldyrev, Sergey V.; Caldarelli, Guido; Zlatić, Vinko; Havlin, Shlomo

2018-05-01

We study secure message-passing in the presence of multiple adversaries in modular networks. We assume a dominant fraction of nodes in each module have the same vulnerability, i.e., the same entity spying on them. We find both analytically and via simulations that the links between the modules (interlinks) have effects analogous to a magnetic field in a spin-system in that for any amount of interlinks the system no longer undergoes a phase transition. We then define the exponents δ, which relates the order parameter (the size of the giant secure component) at the critical point to the field strength (average number of interlinks per node), and γ, which describes the susceptibility near criticality. These are found to be δ = 2 and γ = 1 (with the scaling of the order parameter near the critical point given by β = 1). When two or more vulnerabilities are equally present in a module we find δ = 1 and γ = 0 (with β ≥ 2). Apart from defining a previously unidentified universality class, these exponents show that increasing connections between modules is more beneficial for security than increasing connections within modules. We also measure the correlation critical exponent ν, and the upper critical dimension d c , finding that ν {d}c=3 as for ordinary percolation, suggesting that for secure message-passing d c = 6. These results provide an interesting analogy between secure message-passing in modular networks and the physics of magnetic spin-systems.

Field-Tuned Superconductor-Insulator Transition with and without Current Bias.

PubMed

Bielejec, E; Wu, Wenhao

2002-05-20

The magnetic-field-tuned superconductor-insulator transition has been studied in ultrathin beryllium films quench condensed near 20 K. In the zero-current limit, a finite-size scaling analysis yields the scaling exponent product nuz = 1.35+/-0.10 and a critical sheet resistance, R(c), of about 1.2R(Q), with R(Q) = h/4e(2). However, in the presence of dc bias currents that are smaller than the zero-field critical currents, nuz becomes 0.75+/-0.10. This new set of exponents suggests that the field-tuned transitions with and without a dc bias current belong to different universality classes.

Effect of Zn doping on the magneto-caloric effect and critical constants of Mott insulator MnV{sub 2}O{sub 4}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahi, Prashant; Kumar, A.; Shukla, K. K.

2014-09-15

X-ray absorption near edge spectra (XANES) and magnetization of Zn doped MnV{sub 2}O{sub 4} have been measured and from the magnetic measurement the critical exponents and magnetocaloric effect have been estimated. The XANES study indicates that Zn doping does not change the valence states in Mn and V. It has been shown that the obtained values of critical exponents β, γ and δ do not belong to universal class and the values are in between the 3D Heisenberg model and the mean field interaction model. The magnetization data follow the scaling equation and collapse into two branches indicating that themore » calculated critical exponents and critical temperature are unambiguous and intrinsic to the system. All the samples show large magneto-caloric effect. The second peak in magneto-caloric curve of Mn{sub 0.95}Zn{sub 0.05}V{sub 2}O{sub 4} is due to the strong coupling between orbital and spin degrees of freedom. But 10% Zn doping reduces the residual spins on the V-V pairs resulting the decrease of coupling between orbital and spin degrees of freedom.« less

van der Waals criticality in AdS black holes: A phenomenological study

NASA Astrophysics Data System (ADS)

Bhattacharya, Krishnakanta; Majhi, Bibhas Ranjan; Samanta, Saurav

2017-10-01

Anti-de Sitter black holes exhibit van der Waals-type phase transition. In the extended phase-space formalism, the critical exponents for any spacetime metric are identical to the standard ones. Motivated by this fact, we give a general expression for the Helmholtz free energy near the critical point, which correctly reproduces these exponents. The idea is similar to the Landau model, which gives a phenomenological description of the usual second-order phase transition. Here, two main inputs are taken into account for the analysis: (a) black holes should have van der Waals-like isotherms, and (b) free energy can be expressed solely as a function of thermodynamic volume and horizon temperature. Resulting analysis shows that the form of Helmholtz free energy correctly encapsulates the features of the Landau function. We also discuss the isolated critical point accompanied by nonstandard values of critical exponents. The whole formalism is then extended to two other criticalities, namely, Y -X and T -S (based on the standard; i.e., nonextended phase space), where X and Y are generalized force and displacement, whereas T and S are the horizon temperature and entropy. We observe that in the former case Gibbs free energy plays the role of Landau function, whereas in the later case, that role is played by the internal energy (here, it is the black hole mass). Our analysis shows that, although the existence of a van der Waals phase transition depends on the explicit form of the black hole metric, the values of the critical exponents are universal in nature.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

PubMed

Schnyder, Simon K; Horbach, Jürgen

2018-02-16

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions

NASA Astrophysics Data System (ADS)

Schnyder, Simon K.; Horbach, Jürgen

2018-02-01

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

NASA Astrophysics Data System (ADS)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Activation barrier scaling and crossover for noise-induced switching in micromechanical parametric oscillators.

PubMed

Chan, H B; Stambaugh, C

2007-08-10

We explore fluctuation-induced switching in parametrically driven micromechanical torsional oscillators. The oscillators possess one, two, or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific.

Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lemarie, Gabriel; Delande, Dominique; Chabe, Julien

Using a cold atomic gas exposed to laser pulses - a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies - we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent {nu}=1.59{+-}0.01, which is found to be equal to the one previously computed for themore » Anderson model.« less

Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hohenadler, M.; Aichhorn, M.; Schmidt, S.

2011-10-15

An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott-insulator transition of lattice polaritons. From mean-field and strong-coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid densitymore » and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the three-dimensional XY universality class, analogous to the Bose-Hubbard model.« less

Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior?

NASA Astrophysics Data System (ADS)

Salerno, K. Michael; Maloney, Craig E.; Robbins, Mark O.

2012-09-01

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

Critical scaling analysis for displacive-type organic ferroelectrics around ferroelectric transition

NASA Astrophysics Data System (ADS)

Ding, L. J.

2017-04-01

The critical scaling properties of displacive-type organic ferroelectrics, in which the ferroelectric-paraelectric transition is induced by spin-Peierls instability, are investigated by Green's function theory through the modified Arrott plot, critical isothermal and electrocaloric effect (ECE) analysis around the transition temperature TC. It is shown that the electric entropy change - ΔS follows a power-law dependence of electric field E : - ΔS ∼En with n satisfying the Franco equation n(TC) = 1 +(β - 1) /(β + γ) = 0.618, wherein the obtained critical exponents β = 0.440 and γ = 1.030 are not only corroborated by Kouvel-Fisher method, but also confirm the Widom critical relation δ = 1 + γ / β. The self-consistency and reliability of the obtained critical exponents are further verified by the scaling equations. Additionally, a universal curve of - ΔS is constructed with rescaling temperature and electric field, so that one can extrapolate the ECE in a certain temperature and electric field range, which would be helpful in designing controlled electric refrigeration devices.

Universality in the Self Organized Critical behavior of a cellular model of superconducting vortex dynamics

NASA Astrophysics Data System (ADS)

Sun, Yudong; Vadakkan, Tegy; Bassler, Kevin

2007-03-01

We study the universality and robustness of variants of the simple model of superconducting vortex dynamics first introduced by Bassler and Paczuski in Phys. Rev. Lett. 81, 3761 (1998). The model is a coarse-grained model that captures the essential features of the plastic vortex motion. It accounts for the repulsive interaction between vortices, the pining of vortices at quenched disordered locations in the material, and the over-damped dynamics of the vortices that leads to tearing of the flux line lattice. We report the results of extensive simulations of the critical ``Bean state" dynamics of the model. We find a phase diagram containing four distinct phases of dynamical behavior, including two phases with distinct Self Organized Critical (SOC) behavior. Exponents describing the avalanche scaling behavior in the two SOC phases are determined using finite-size scaling. The exponents are found to be robust within each phase and for different variants of the model. The difference of the scaling behavior in the two phases is also observed in the morphology of the avalanches.

A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

NASA Astrophysics Data System (ADS)

Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiang-Gang

We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point J2c1 = 0 . 53 (1) J1 and the critical exponents β = 0 . 50 (4) . In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents ν = 0 . 68 (3) and ηs = 0 . 34 (6) , which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at J2c1 = 0 . 53 (1) J1 . This project is supported by the EU Strep project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM; and the Institute for Quantum Information and Matter.

Two-dimensional Ising model on random lattices with constant coordination number

NASA Astrophysics Data System (ADS)

Schrauth, Manuel; Richter, Julian A. J.; Portela, Jefferson S. E.

2018-02-01

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014), 10.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

Influence of grain size and sintering temperature grain size on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.67Sr0.33MnO3 nanoparticles

NASA Astrophysics Data System (ADS)

Baaziz, H.; Tozri, A.; Dhahri, E.; Hlil, E. K.

2018-03-01

We have undertaken a systematic study of critical behavior in La0.67Sr0.33MnO3 nanoparticles, sintered at different temperatures (L6, L8, L10 and L12 sintered at 600 °C, 800 °C, 1000 °C, 1200 °C respectively), by magnetization measurements. The critical exponents are estimated by various techniques such as the Modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. Compared to standard models, the critical exponents are close to those expected by the Mean-field model (with β = 0.5 γ = 1, and δ = 3) for (L6, L8, and L10) samples and by the (3D) Heisenberg model (β = 0.365, γ = 1.336 and δ = 4.80) for L12 sample. We conclude that the reduction of grain size strongly influences the universality class.

Percolation of spatially constraint networks

NASA Astrophysics Data System (ADS)

Li, Daqing; Li, Guanliang; Kosmidis, Kosmas; Stanley, H. E.; Bunde, Armin; Havlin, Shlomo

2011-03-01

We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)~r-δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

Universal Critical Dynamics in High Resolution Neuronal Avalanche Data

NASA Astrophysics Data System (ADS)

Friedman, Nir; Ito, Shinya; Brinkman, Braden A. W.; Shimono, Masanori; DeVille, R. E. Lee; Dahmen, Karin A.; Beggs, John M.; Butler, Thomas C.

2012-05-01

The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

Evidence of a Critical Phase Transition in Purely Temporal Dynamics with Long-Delayed Feedback

NASA Astrophysics Data System (ADS)

Faggian, Marco; Ginelli, Francesco; Marino, Francesco; Giacomelli, Giovanni

2018-04-01

Experimental evidence of an absorbing phase transition, so far associated with spatiotemporal dynamics, is provided in a purely temporal optical system. A bistable semiconductor laser, with long-delayed optoelectronic feedback and multiplicative noise, shows the peculiar features of a critical phenomenon belonging to the directed percolation universality class. The numerical study of a simple, effective model provides accurate estimates of the transition critical exponents, in agreement with both theory and our experiment. This result pushes forward a hard equivalence of nontrivial stochastic, long-delayed systems with spatiotemporal ones and opens a new avenue for studying out-of-equilibrium universality classes in purely temporal dynamics.

Critical behavior of magnetization in URhAl: Quasi-two-dimensional Ising system with long-range interactions

NASA Astrophysics Data System (ADS)

Tateiwa, Naoyuki; Pospíšil, Jiří; Haga, Yoshinori; Yamamoto, Etsuji

2018-02-01

The critical behavior of dc magnetization in the uranium ferromagnet URhAl with the hexagonal ZrNiAl-type crystal structure has been studied around the ferromagnetic transition temperature TC. The critical exponent β for the temperature dependence of the spontaneous magnetization below TC,γ for the magnetic susceptibility, and δ for the magnetic isotherm at TC, have been obtained with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. We have determined the critical exponents as β =0.287 ±0.005 , γ =1.47 ±0.02 , and δ =6.08 ±0.04 by the scaling analysis and the critical isotherm analysis. These critical exponents satisfy the Widom scaling law δ =1 +γ /β . URhAl has strong uniaxial magnetic anisotropy, similar to its isostructural UCoAl that has been regarded as a three-dimensional (3D) Ising system in previous studies. However, the universality class of the critical phenomenon in URhAl does not belong to the 3D Ising model (β =0.325 , γ =1.241 , and δ =4.82 ) with short-range exchange interactions between magnetic moments. The determined exponents can be explained with the results of the renormalization group approach for a two-dimensional (2D) Ising system coupled with long-range interactions decaying as J (r ) ˜r-(d +σ ) with σ =1.44 . We suggest that the strong hybridization between the uranium 5 f and rhodium 4 d electrons in the U-RhI layer in the hexagonal crystal structure is a source of the low-dimensional magnetic property. The present result is contrary to current understandings of the physical properties in a series of isostructural UTX uranium ferromagnets (T: transition metals, X: p -block elements) based on the 3D Ising model.

Conductivity fluctuations in polymer's networks

NASA Astrophysics Data System (ADS)

Samukhin, A. N.; Prigodin, V. N.; Jastrabík, L.

1998-01-01

A Polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + ε close to one. Percolation model on such a fractal is studied. Using real space renormalization group approach of Migdal and Kadanoff, we find the threshold value and all the critical exponents in the percolation model to be strongly nonanalytic functions of ε, e.g. the critical exponent of the conductivity was obtained to be ε-2 exp (-1 - 1/ε). The main part of the finite-size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable which is proportional to a large power of the conductivity, but with ε-dependent low-conductivity cut-off. Its reduced central momenta are of the order of e -1/ε up to a very high order.

Universal depinning transition of domain walls in ultrathin ferromagnets

NASA Astrophysics Data System (ADS)

Diaz Pardo, R.; Savero Torres, W.; Kolton, A. B.; Bustingorry, S.; Jeudy, V.

2017-05-01

We present a quantitative and comparative study of magnetic-field-driven domain-wall depinning transition in different ferromagnetic ultrathin films over a wide range of temperature. We reveal a universal scaling function accounting for both drive and thermal effects on the depinning transition, including critical exponents. The consistent description we obtain for both the depinning and subthreshold thermally activated creep motion should shed light on the universal glassy dynamics of thermally fluctuating elastic objects pinned by disordered energy landscapes.

Photon orbits and thermodynamic phase transition of d -dimensional charged AdS black holes

NASA Astrophysics Data System (ADS)

Wei, Shao-Wen; Liu, Yu-Xiao

2018-05-01

We study the relationship between the null geodesics and thermodynamic phase transition for the charged AdS black hole. In the reduced parameter space, we find that there exist nonmonotonic behaviors of the photon sphere radius and the minimum impact parameter for the pressure below its critical value. The study also shows that the changes of the photon sphere radius and the minimum impact parameter can serve as order parameters for the small-large black hole phase transition. In particular, these changes have an universal exponent of 1/2 near the critical point for any dimension d of spacetime. These results imply that there may exist universal critical behavior of gravity near the thermodynamic critical point of the black hole system.

Universal thermodynamics of the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here, by solving the thermodynamic Bethe ansatz equations, we study the universal thermodynamics, quantum criticality, and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures, and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent z =2 and correlation critical exponent ν =1 /2 in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.

Hydropathic self-organized criticality: a magic wand for protein physics.

PubMed

Phillips, J C

2012-10-01

Self-organized criticality (SOC) is a popular concept that has been the subject of more than 3000 articles in the last 25 years. The characteristic signature of SOC is the appearance of self-similarity (power-law scaling) in observable properties. A characteristic observable protein property that describes protein-water interactions is the water-accessible (hydropathic) interfacial area of compacted globular protein networks. Here we show that hydropathic power-law (size- or length-scale-dependent) exponents derived from SOC enable theory to connect standard Web-based (BLAST) short-range amino acid (aa) sequence similarities to long-range aa sequence hydropathic roughening form factors that hierarchically describe evolutionary trends in water - membrane protein interactions. Our method utilizes hydropathic aa exponents that define a non-Euclidean metric realistically rooted in the atomic coordinates of 5526 protein segments. These hydropathic aa exponents thereby encapsulate universal (but previously only implicit) non-Euclidean long-range differential geometrical features of the Protein Data Bank. These hydropathic aa exponents easily organize small mutated aa sequence differences between human and proximate species proteins. For rhodopsin, the most studied transmembrane signaling protein associated with night vision, analysis shows that this approach separates Euclidean short- and non-Euclidean long-range aa sequence properties, and shows that they correlate with 96% success for humans, monkeys, cats, mice and rabbits. Proper application of SOC using hydropathic aa exponents promises unprecedented simplifications of exponentially complex protein sequence-structure-function problems, both conceptual and practical.

Crossover phenomena in the critical range near magnetic ordering transition

NASA Astrophysics Data System (ADS)

Köbler, U.

2018-05-01

Among the most important issues of Renormalization Group (RG) theory are crossover events and relevant (or non-relevant) interactions. These terms are unknown to atomistic theories but they will be decisive for future field theories of magnetism. In this experimental study the importance of these terms for the critical dynamics above and below magnetic ordering transition is demonstrated on account of new analyses of published data. When crossover events are overlooked and critical data are fitted by a single power function of temperature over a temperature range including a crossover event, imprecise critical exponents result. The rather unsystematic and floating critical exponents reported in literature seem largely to be due to this problem. It is shown that for appropriate data analyses critical exponents are obtained that are to a good approximation rational numbers. In fact, rational critical exponents can be expected when spin dynamics is controlled by the bosons of the continuous magnetic medium (Goldstone bosons). The bosons are essentially magnetic dipole radiation generated by the precessing spins. As a result of the here performed data analyses, critical exponents for the magnetic order parameter of β = 1/2, 1/3, 1/4 and 1/6 are obtained. For the critical paramagnetic susceptibility the exponents are γ = 1 and γ = 4/3.

Griffiths-like phase, critical behavior near the paramagnetic-ferromagnetic phase transition and magnetic entropy change of nanocrystalline La0.75Ca0.25MnO3

NASA Astrophysics Data System (ADS)

Phong, P. T.; Ngan, L. T. T.; Dang, N. V.; Nguyen, L. H.; Nam, P. H.; Thuy, D. M.; Tuan, N. D.; Bau, L. V.; Lee, I. J.

2018-03-01

In this work, we report the structural and magnetic properties of La0.75Ca0.25MnO3 nanoparticles synthesized by the sol-gel route. Rietvield refinement of X-ray powder diffraction confirms that our sample is single phase and crystallizes in orthorhombic system with Pnma space group. The facts that effective magnetic moment is large and the inverse susceptibility deviates from the Curie Weiss lawn indicate the presence of Griffiths-like cluster phase. The critical exponents have been estimated using different techniques such as modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. The critical exponents values of La0.75Ca0.25MnO3 are very close to those found out by the mean-field model, and this can be explained by the existence of a long-range interactions between spins in this system. These results were in good agreement with those obtained using the critical exponents of magnetic entropy change. The self-consistency and reliability of the critical exponent was verified by the Widom scaling law and the universal scaling hypothesis. Using the Harris criterion, we deduced that the disorder is relevant in our case. The maximum magnetic entropy change (ΔSM) calculated from the M-H measurements is 3.47 J/kg K under an external field change of 5 T. The ΔSM-T curves collapsed onto a single master curve regardless of the composition and the applied field, confirming the magnetic ordering is of second order nature. The obtained result was compared to ones calculated based on the Arrott plot and a good concordance is observed. Moreover, the spontaneous magnetization obtained from the entropy change is in excellent agreement with that deduced by classically extrapolation the Arrott curves. This result confirms the validity of the estimation of the spontaneous magnetization using the magnetic entropy change.

Superconductor-Metal-Insulator transition in two dimensional Ta thin Films

NASA Astrophysics Data System (ADS)

Park, Sun-Gyu; Kim, Eunseong

2013-03-01

Superconductor-insulator transition has been induced by tuning film thickness or magnetic field. Recent electrical transport measurements of MoGe, Bi, Ta thin films revealed an interesting intermediate metallic phase which intervened superconducting and insulating phases at certain range of magnetic field. Especially, Ta thin films show the characteristic IV behavior at each phase and the disorder tuned intermediate metallic phase [Y. Li, C. L. Vicente, and J. Yoon, Physical Review B 81, 020505 (2010)]. This unexpected metallic phase can be interpreted as a consequence of vortex motion or contribution of fermionic quasiparticles. In this presentation, we report the scaling behavior during the transitions in Ta thin film as well as the transport measurements in various phases. Critical exponents v and z are obtained in samples with wide ranges of disorder. These results reveal new universality class appears when disorder exceeds a critical value. Dynamical exponent z of Superconducting sample is found to be 1, which is consistent with theoretical prediction of unity. z in a metallic sample is suddenly increased to be approximately 2.5. This critical exponent is much larger than the value found in other system and theoretical prediction. We gratefully acknowledge the financial support by the National Research Foundation of Korea through the Creative Research Initiatives.

Insulating phase in Sr2IrO4: An investigation using critical analysis and magnetocaloric effect

NASA Astrophysics Data System (ADS)

Bhatti, Imtiaz Noor; Pramanik, A. K.

2017-01-01

The nature of insulating phase in 5d based Sr2IrO4 is quite debated as the theoretical as well as experimental investigations have put forward evidences in favor of both magnetically driven Slater-type and interaction driven Mott-type insulator. To understand this insulating behavior, we have investigated the nature of magnetic state in Sr2IrO4 through studying critical exponents, low temperature thermal demagnetization and magnetocaloric effect. The estimated critical exponents do not exactly match with any universality class, however, the values obey the scaling behavior. The exponent values suggest that spin interaction in present material is close to mean-field model. The analysis of low temperature thermal demagnetization data, however, shows dual presence of localized- and itinerant-type of magnetic interaction. Moreover, field dependent change in magnetic entropy indicates magnetic interaction is close to mean-field type. While this material shows an insulating behavior across the magnetic transition, yet a distinct change in slope in resistivity is observed around Tc. We infer that though the insulating phase in Sr2IrO4 is more close to be Slater-type but the simultaneous presence of both Slater- and Mott-type is the likely scenario for this material.

Magnetocaloric effect and critical field analysis in Eu substituted La0.7-xEuxSr0.3MnO3 (x = 0.0, 0.1, 0.2, 0.3) manganites

NASA Astrophysics Data System (ADS)

Vadnala, Sudharshan; Asthana, Saket

2018-01-01

In this study, we have investigated magnetic behavior, magnetocaloric effect and critical exponent analysis of La0.7-xEuxSr0.3MnO3 (x = 0.0, 0.1, 0.2, 0.3) manganites synthesized through solid state reaction route. The crystallographic data obtained from refinement of X-ray diffraction patterns reveal that crystal structure changes from rhombohedral (for x = 0.0) to orthorhombic (for x ≥ 0.1). The average ionic radius of A-site is decreased from 1.384 Å (for x = 0.0) to 1.360 Å (for x = 0.3) with Eu3+ substitution which in turn decreases the Mn-O-Mn bond angles. Magnetization measurements are performed in the vicinity of TC to determine magnetocaloric effect (MCE) and critical field behavior. The maximum magnetic entropy change (Δ SMmax) (for μ0ΔH = 6T) increases with the Eu3+ substitution from 3.88 J/kg K (for x = 0.0) to 5.03 J/kg K (for x = 0.3) at the transition temperature. The critical field behaviour of compounds was analysed using various methods such as modified Arrott plots, Kouvel-Fisher method and critical isotherm to determine critical temperature and critical exponents (β, γ and δ). The obtained critical exponents are in good accordance with scaling relation. The temperature dependence of the order parameter n, for different magnetic fields, is studied using the relation ΔSMαHn. The values of n are found to obey the Curie-Weiss law for temperatures above the transition temperature. The rescaled change in entropy data for all compounds collapses into the same universal curve, revealing a second order phase transition.

Surface critical behavior of thin Ising films at the ‘special point’

NASA Astrophysics Data System (ADS)

Moussa, Najem; Bekhechi, Smaine

2003-03-01

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Scaling properties of a rice-pile model: inertia and friction effects.

PubMed

Khfifi, M; Loulidi, M

2008-11-01

We present a rice-pile cellular automaton model that includes inertial and friction effects. This model is studied in one dimension, where the updating of metastable sites is done according to a stochastic dynamics governed by a probabilistic toppling parameter p that depends on the accumulated energy of moving grains. We investigate the scaling properties of the model using finite-size scaling analysis. The avalanche size, the lifetime, and the residence time distributions exhibit a power-law behavior. Their corresponding critical exponents, respectively, tau, y, and yr, are not universal. They present continuous variation versus the parameters of the system. The maximal value of the critical exponent tau that our model gives is very close to the experimental one, tau=2.02 [Frette, Nature (London) 379, 49 (1996)], and the probability distribution of the residence time is in good agreement with the experimental results. We note that the critical behavior is observed only in a certain range of parameter values of the system which correspond to low inertia and high friction.

Universality, twisted fans, and the Ising model. [Renormalization, two-loop calculations, scale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dash, J.W.; Harrington, S.J.

1975-06-24

Critical exponents are evaluated for the Ising model using universality in the form of ''twisted fans'' previously introduced in Reggeon field theory. The universality is with respect to scales induced through renormalization. Exact twists are obtained at ..beta.. = 0 in one loop for D = 2,3 with ..nu.. = 0.75 and 0.60 respectively. In two loops one obtains ..nu.. approximately 1.32 and 0.68. No twists are obtained for eta, however. The results for the standard two loop calculations are also presented as functions of a scale.

Majority-Vote Model with Heterogeneous Agents on Square Lattice

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2013-11-01

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of [M. J. Oliveira, J. Stat. Phys.66, 273 (1992)] with heterogeneous agents on square lattice (SL). By Monte Carlo (MC) simulations and finite-size scaling relations, the critical exponents β/ν, γ/ν and 1/ν and points qc and U* are obtained. After extensive simulations, we obtain β/ν = 0.35(1), γ/ν = 1.23(8) and 1/ν = 1.05(5). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.1589(4) and U* = 0.604(7). Within the error bars, the exponents obey the relation 2β/ν + γ/ν = 2 and the results presented here demonstrate that the MVM heterogeneous agents belongs to a different universality class than the nonequilibrium MVM with homogeneous agents on SL.

Majority-Vote Model on Opinion-Dependent Network

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2013-09-01

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of Oliveira 1992 on opinion-dependent network or Stauffer-Hohnisch-Pittnauer (SHP) networks. By Monte Carlo (MC) simulations and finite-size scaling relations the critical exponents β/ν, γ/ν and 1/ν and points qc and U* are obtained. After extensive simulations, we obtain β/ν = 0.230(3), γ/ν = 0.535(2) and 1/ν = 0.475(8). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.166(3) and U* = 0.288(3). Within the error bars, the exponents obey the relation 2β/ν + γ/ν = 1 and the results presented here demonstrate that the MVM belongs to a different universality class than the equilibrium Ising model on SHP networks, but to the same class as majority-vote models on some other networks.

Nonlinear Midinfrared Photothermal Spectroscopy Using Zharov Splitting and Quantum Cascade Lasers.

PubMed

Mertiri, Alket; Altug, Hatice; Hong, Mi K; Mehta, Pankaj; Mertz, Jerome; Ziegler, Lawrence D; Erramilli, Shyamsunder

2014-08-20

We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-octyl-4'-cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical bifurcation. The bifurcation, observed in heterodyne two-color pump-probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as a function of absorbed infrared power shows the bifurcation has a critical exponent of 0.5. The observation of an apparently universal critical exponent in a nonequilibrium state is explained using an analytical model analogous of mean field theory. Apart from the intrinsic interest for nonequilibrium studies, nonlinear photothermal methods lead to a dramatic narrowing of spectral lines, giving rise to a potential new contrast mechanism for the rapidly emerging new field of mid-infrared microspectroscopy using QCLs.

Nonlinear Midinfrared Photothermal Spectroscopy Using Zharov Splitting and Quantum Cascade Lasers

PubMed Central

2015-01-01

We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-octyl-4′-cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical bifurcation. The bifurcation, observed in heterodyne two-color pump–probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as a function of absorbed infrared power shows the bifurcation has a critical exponent of 0.5. The observation of an apparently universal critical exponent in a nonequilibrium state is explained using an analytical model analogous of mean field theory. Apart from the intrinsic interest for nonequilibrium studies, nonlinear photothermal methods lead to a dramatic narrowing of spectral lines, giving rise to a potential new contrast mechanism for the rapidly emerging new field of mid-infrared microspectroscopy using QCLs. PMID:25541620

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

Dynamic behavior of the interface of striplike structures in driven lattice gases

NASA Astrophysics Data System (ADS)

Saracco, Gustavo P.; Albano, Ezequiel V.

2008-09-01

In this work, the dynamic behavior of the interfaces in both the standard and random driven lattice gas models (DLG and RDLG, respectively) is investigated via numerical Monte Carlo simulations in two dimensions. These models consider a lattice gas of density ρ=1/2 with nearest-neighbor attractive interactions between particles under the influence of an external driven field applied along one fixed direction in the case of the DLG model, and a randomly varying direction in the case of the RDLG model. The systems are also in contact with a reservoir at temperature T . Those systems undergo a second-order nonequilibrium phase transition between an ordered state characterized by high-density strips crossing the sample along the driving field, and a quasilattice gas disordered state. For T≲Tc , the average interface width of the strips (W) was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value Wsat2 only depends on the lattice size parallel to the external field axis Ly and exhibits two distinct regimes: Wsat2∝lnLy for low temperatures, that crosses over to Wsat2∝Ly2αI near the critical zone, αI=1/2 being the roughness exponent of the interface. By using the relationship αI=1/(1+ΔI) , the anisotropic exponent for the interface of the DLG model was estimated, giving ΔI≃1 , in agreement with the computed value for anisotropic bulk exponent ΔB in a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of W at Tc was also monitored and shows two growing stages: first one observes that W∝lnt for several decades, and in the following times one has W∝tβI , where βI is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving z⊥I≈4 , which is consistent with the dynamic exponent of the bulk critical transition z⊥B in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.

Localization in a quantum spin Hall system.

PubMed

Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto

2007-02-16

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.

Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique

NASA Astrophysics Data System (ADS)

Garcia-Adeva, Angel J.; Huber, David L.

2001-07-01

In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.

Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions

DOE PAGES

Rademaker, Louk; Vinokur, Valerii M.; Galda, Alexey

2017-03-16

Here, we study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions.

PubMed

Rademaker, Louk; Vinokur, Valerii M; Galda, Alexey

2017-03-16

We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

Turbidity determination of the critical exponent eta in the liquid-liquid mixture methanol and cyclohexane.

PubMed

Lytle, Amy; Jacobs, D T

2004-03-22

The turbidity of the liquid-liquid mixture methanol-cyclohexane has been measured very near its critical point and used to test competing theoretical predictions and to determine the critical correlation-correction exponent eta. By measuring the ratio of the transmitted to incident light intensities over five decades in reduced temperature, we are able to determine that Ferrell's theoretical prediction for the turbidity explains the data with the correlation length amplitude xi0=0.330+/-0.003 nm and critical exponents eta=0.041+/-0.005 and nu=0.632+/-0.002. These values are consistent with the values measured before for xi0 in this system and with the exponents predicted by theory. The data allow five different theoretical expressions to be tested and to select two as being equivalent when very close to the critical point. (c) 2004 American Institute of Physics

Coherent forward scattering as a signature of Anderson metal-insulator transitions

NASA Astrophysics Data System (ADS)

Ghosh, Sanjib; Miniatura, Christian; Cherroret, Nicolas; Delande, Dominique

2017-04-01

We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder.

Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

César Mansur Filho, Júlio; Dickman, Ronald

2011-05-01

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32 000 sites. The resulting estimates for critical exponents β, \\beta /\

Scaling functions for systems with finite range of interaction

NASA Astrophysics Data System (ADS)

Sampaio-Filho, C. I. N.; Moreira, F. G. B.

2013-09-01

We present a numerical determination of the scaling functions of the magnetization, the susceptibility, and the Binder's cumulant for two nonequilibrium model systems with varying range of interactions. We consider Monte Carlo simulations of the block voter model (BVM) on square lattices and of the majority-vote model (MVM) on random graphs. In both cases, the satisfactory data collapse obtained for several system sizes and interaction ranges supports the hypothesis that these functions are universal. Our analysis yields an accurate estimation of the long-range exponents, which govern the decay of the critical amplitudes with the range of interaction, and is consistent with the assumption that the static exponents are Ising-like for the BVM and classical for the MVM.

Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

Indications for a critical point in the phase diagram for hot and dense nuclear matter

NASA Astrophysics Data System (ADS)

Lacey, Roy A.

2016-12-01

Two-pion interferometry measurements are studied for a broad range of collision centralities in Au+Au (√{sNN} = 7.7- 200 GeV) and Pb+Pb (√{sNN} = 2.76 TeV) collisions. They indicate non-monotonic excitation functions for the Gaussian emission source radii difference (Rout -Rside), suggestive of reaction trajectories which spend a fair amount of time near a soft point in the equation of state (EOS) that coincides with the critical end point (CEP). A Finite-Size Scaling (FSS) analysis of these excitation functions, provides further validation tests for the CEP. It also indicates a second order phase transition at the CEP, and the values Tcep ∼ 165 MeV and μBcep ∼ 95 MeV for its location in the (T ,μB)-plane of the phase diagram. The static critical exponents (ν ≈ 0.66 and γ ≈ 1.2) extracted via the same FSS analysis, place this CEP in the 3D Ising model (static) universality class. A Dynamic Finite-Size Scaling analysis of the excitation functions, gives the estimate z ∼ 0.87 for the dynamic critical exponent, suggesting that the associated critical expansion dynamics is dominated by the hydrodynamic sound mode.

Statistical Systems with Z

NASA Astrophysics Data System (ADS)

William, Peter

In this dissertation several two dimensional statistical systems exhibiting discrete Z(n) symmetries are studied. For this purpose a newly developed algorithm to compute the partition function of these models exactly is utilized. The zeros of the partition function are examined in order to obtain information about the observable quantities at the critical point. This occurs in the form of critical exponents of the order parameters which characterize phenomena at the critical point. The correlation length exponent is found to agree very well with those computed from strong coupling expansions for the mass gap and with Monte Carlo results. In Feynman's path integral formalism the partition function of a statistical system can be related to the vacuum expectation value of the time ordered product of the observable quantities of the corresponding field theoretic model. Hence a generalization of ordinary scale invariance in the form of conformal invariance is focussed upon. This principle is very suitably applicable, in the case of two dimensional statistical models undergoing second order phase transitions at criticality. The conformal anomaly specifies the universality class to which these models belong. From an evaluation of the partition function, the free energy at criticality is computed, to determine the conformal anomaly of these models. The conformal anomaly for all the models considered here are in good agreement with the predicted values.

Depinning transition of a domain wall in ferromagnetic films

DOE PAGES

Xi, Bin; Luo, Meng -Bo; Vinokur, Valerii M.; ...

2015-09-14

Here, we report first principle numerical study of domain wall (DW) depinning in two-dimensional magnetic film, which is modeled by 2D random-field Ising system with the dipole-dipole interaction. We observe non-conventional activation-type motion of DW and reveal the fractal structure of DW near the depinning transition. We determine scaling functions describing critical dynamics near the transition and obtain universal exponents establishing connection between thermal softening of pinning potential and critical dynamics. In addition, we observe that tuning the strength of the dipole-dipole interaction switches DW dynamics between two different universality classes, corresponding to two distinct dynamic regimes characterized by non-Arrheniusmore » and conventional Arrhenius-type DW motions.« less

Moving line model and avalanche statistics of Bingham fluid flow in porous media.

PubMed

Chevalier, Thibaud; Talon, Laurent

2015-07-01

In this article, we propose a simple model to understand the critical behavior of path opening during flow of a yield stress fluid in porous media as numerically observed by Chevalier and Talon (2015). This model can be mapped to the problem of a contact line moving in an heterogeneous field. Close to the critical point, this line presents an avalanche dynamic where the front advances by a succession of waiting time and large burst events. These burst events are then related to the non-flowing (i.e. unyielded) areas. Remarkably, the statistics of these areas reproduce the same properties as in the direct numerical simulations. Furthermore, even if our exponents seem to be close to the mean field universal exponents, we report an unusual bump in the distribution which depends on the disorder. Finally, we identify a scaling invariance of the cluster spatial shape that is well fit, to first order, by a self-affine parabola.

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

NASA Astrophysics Data System (ADS)

Dashti-Naserabadi, H.; Najafi, M. N.

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems.

PubMed

Dashti-Naserabadi, H; Najafi, M N

2017-10-01

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d-dimensional cross sections and the d-dimensional BTW model for d=2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.

Scaling functions for the Inverse Compressibility near the QCD critical point

NASA Astrophysics Data System (ADS)

Lacey, Roy

2017-09-01

The QCD phase diagram can be mapped out by studying fluctuations and their response to changes in the temperature and baryon chemical potential. Theoretical studies indicate that the cumulant ratios Cn /Cm used to characterize the fluctuation of conserved charges, provide a valuable probe of deconfinement and chiral dynamics, as well as for identifying the position of the critical endpoint (CEP) in the QCD phase diagram. The ratio C1 /C2 , which is linked to the inverse compressibility, vanishes at the CEP due to the divergence of the net quark number fluctuations at the critical point belonging to the Z(2) universality class. Therefore, it's associated scaling function can give insight on the location of the critical end point, as well as the critical exponents required to assign its static universality class. Scaling functions for the ratio C1 /C2 , obtained from net-proton multiplicity distributions for a broad range of collision centralities in Au+Au (√{sNN} = 7.7 - 200 GeV) collisions will be presented and discussed.

The Kibble-Zurek mechanism in phase transitions of non-equilibrium systems

NASA Astrophysics Data System (ADS)

Cheung, Hil F. H.; Patil, Yogesh S.; Date, Aditya G.; Vengalattore, Mukund

2017-04-01

We experimentally realize a driven-dissipative phase transition using a mechanical parametric amplifier to demonstrate key signatures of a second order phase transition, including a point where the susceptibilities and relaxation time scales diverge, and where the system exhibits a spontaneous breaking of symmetry. Though reminiscent of conventional equilibrium phase transitions, it is unclear if such driven-dissipative phase transitions are amenable to the conventional Landau-Ginsburg-Wilson paradigm, which relies on concepts of scale invariance and universality, and recent work has shown that such phase transitions can indeed lie beyond such conventional universality classes. By quenching the system past the critical point, we investigate the dynamics of the emergent ordered phase and find that our measurements are in excellent agreement with the Kibble-Zurek mechanism. In addition to verifying the Kibble-Zurek hypothesis in driven-dissipative phase transitions for the first time, we also demonstrate that the measured critical exponents accurately reflect the interplay between intrinsic coherent dynamics and environmental correlations, showing a clear departure from mean field exponents in the case of non-Markovian system-bath interactions. We further discuss how reservoir engineering and the imposition of artificial environmental correlations can result in the stabilization of novel many-body quantum phases and aid in the creation of exotic non-equilibrium states of matter.

Strong-coupling analysis of two-dimensional O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campostrini, M.; Pelissetto, A.; Rossi, P.

1996-09-01

The critical behavior of two-dimensional (2D) O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green{close_quote}s function {ital G}({ital x}), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For {ital N}{lt}2 the critical behavior is of power-law type, and the exponents {gamma} and {nu} extracted from our strong-coupling analysis confirm exact results derived assuming universality with solvable solid-on-solid models. At {ital N}=2, i.e., for the 2D {ital XY} model,more » the results from all lattices considered are consistent with the Kosterlitz-Thouless exponential approach to criticality, characterized by an exponent {sigma}=1/2, and with universality. The value {sigma}=1/2 is confirmed within an uncertainty of few percent. The prediction {eta}=1/4 is also roughly verified. For various values of {ital N}{le}2, we determine some ratios of amplitudes concerning the two-point function {ital G}({ital x}) in the critical limit of the symmetric phase. This analysis shows that the low-momentum behavior of {ital G}({ital x}) in the critical region is essentially Gaussian at all values of {ital N}{le}2. Exact results for the long-distance behavior of {ital G}({ital x}) when {ital N}=1 (Ising model in the strong-coupling phase) confirm this statement. {copyright} {ital 1996 The American Physical Society.}« less

Phase transition in the parametric natural visibility graph.

PubMed

Snarskii, A A; Bezsudnov, I V

2016-10-01

We investigate time series by mapping them to the complex networks using a parametric natural visibility graph (PNVG) algorithm that generates graphs depending on arbitrary continuous parameter-the angle of view. We study the behavior of the relative number of clusters in PNVG near the critical value of the angle of view. Artificial and experimental time series of different nature are used for numerical PNVG investigations to find critical exponents above and below the critical point as well as the exponent in the finite size scaling regime. Altogether, they allow us to find the critical exponent of the correlation length for PNVG. The set of calculated critical exponents satisfies the basic Widom relation. The PNVG is found to demonstrate scaling behavior. Our results reveal the similarity between the behavior of the relative number of clusters in PNVG and the order parameter in the second-order phase transitions theory. We show that the PNVG is another example of a system (in addition to magnetic, percolation, superconductivity, etc.) with observed second-order phase transition.

Critical exponents of the explosive percolation transition

NASA Astrophysics Data System (ADS)

da Costa, R. A.; Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F.

2014-04-01

In a new type of percolation phase transition, which was observed in a set of nonequilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential merging of small components and delays the emergence of the percolation cluster. First simulations led to a conclusion that a percolation cluster in this irreversible process is born discontinuously, by a discontinuous phase transition, which results in the term "explosive percolation transition." We have shown that this transition is actually continuous (second order) though with an anomalously small critical exponent of the percolation cluster. Here we propose an efficient numerical method enabling us to find the critical exponents and other characteristics of this second-order transition for a representative set of explosive percolation models with different number of choices. The method is based on gluing together the numerical solutions of evolution equations for the cluster size distribution and power-law asymptotics. For each of the models, with high precision, we obtain critical exponents and the critical point.

The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Heydenreich, Markus; Kolesnikov, Leonid

2018-04-01

We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).

Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the Lifshitz black hole background

NASA Astrophysics Data System (ADS)

Sherkatghanad, Z.; Mirza, B.; Lalehgani Dezaki, F.

We analytically describe the properties of the s-wave holographic superconductor with the exponential nonlinear electrodynamics in the Lifshitz black hole background in four-dimensions. Employing an assumption the scalar and gauge fields backreact on the background geometry, we calculate the critical temperature as well as the condensation operator. Based on Sturm-Liouville method, we show that the critical temperature decreases with increasing exponential nonlinear electrodynamics and Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. Also we find that the effects of backreaction has a more important role on the critical temperature and condensation operator in small values of Lifshitz dynamical exponent, while z is around one. In addition, the properties of the upper critical magnetic field in Lifshitz black hole background using Sturm-Liouville approach is investigated to describe the phase diagram of the corresponding holographic superconductor in the probe limit. We observe that the critical magnetic field decreases with increasing Lifshitz dynamical exponent, z, and it goes to zero at critical temperature, independent of the Lifshitz dynamical exponent, z.

Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing

NASA Astrophysics Data System (ADS)

Durang, Xavier; Henkel, Malte

2017-12-01

Motivated by an analogy with the spherical model of a ferromagnet, the three Arcetri models are defined. They present new universality classes, either for the growth of interfaces, or else for lattice gases. They are distinct from the common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Their non-equilibrium evolution can be studied by the exact computation of their two-time correlators and responses. In both interpretations, the first model has a critical point in any dimension and shows simple ageing at and below criticality. The exact universal exponents are found. The second and third model are solved at zero temperature, in one dimension, where both show logarithmic sub-ageing, of which several distinct types are identified. Physically, the second model describes a lattice gas and the third model describes interface growth. A clear physical picture on the subsequent time and length scales of the sub-ageing process emerges.

Criticality of the mean-field spin-boson model: boson state truncation and its scaling analysis

NASA Astrophysics Data System (ADS)

Hou, Y.-H.; Tong, N.-H.

2010-11-01

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents β and δ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states N b . We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in 0 < s < 1/2 and incurs the deviation of the exponents from the classical values. The magnetization at zero bias near the critical point is described by a generalized homogeneous function (GHF) of two variables τ = α - α c and x = 1/ N b . The universal function has a double-power form and the powers are obtained analytically as well as numerically. Similarly, m( α = α c ) is found to be a GHF of γ and x. In the regime s > 1/2, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

NASA Astrophysics Data System (ADS)

Benhaiem, David; Joyce, Michael; Sicard, François

2013-03-01

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two-point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the `stable clustering' region from the `universal' region is very well approximated by a `critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of `universality' of non-linear clustering in this context.

Critical behavior and dimension crossover of pion superfluidity

NASA Astrophysics Data System (ADS)

Wang, Ziyue; Zhuang, Pengfei

2016-09-01

We investigate the critical behavior of pion superfluidity in the framework of the functional renormalization group (FRG). By solving the flow equations in the SU(2) linear sigma model at finite temperature and isospin density, and making comparison with the fixed point analysis of a general O (N ) system with continuous dimension, we find that the pion superfluidity is a second order phase transition subject to an O (2 ) universality class with a dimension crossover from dc=4 to dc=3 . This phenomenon provides a concrete example of dimension reduction in thermal field theory. The large-N expansion gives a temperature independent critical exponent β and agrees with the FRG result only at zero temperature.

Criticality in Neuronal Networks

NASA Astrophysics Data System (ADS)

Friedman, Nir; Ito, Shinya; Brinkman, Braden A. W.; Shimono, Masanori; Deville, R. E. Lee; Beggs, John M.; Dahmen, Karin A.; Butler, Tom C.

2012-02-01

In recent years, experiments detecting the electrical firing patterns in slices of in vitro brain tissue have been analyzed to suggest the presence of scale invariance and possibly criticality in the brain. Much of the work done however has been limited in two ways: 1) the data collected is from local field potentials that do not represent the firing of individual neurons; 2) the analysis has been primarily limited to histograms. In our work we examine data based on the firing of individual neurons (spike data), and greatly extend the analysis by considering shape collapse and exponents. Our results strongly suggest that the brain operates near a tuned critical point of a highly distinctive universality class.

Critical decay exponent of the pair contact process with diffusion

NASA Astrophysics Data System (ADS)

Park, Su-Chan

2014-11-01

We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent δ . To obtain an accurate estimate of δ , we first find the strength of corrections to scaling using the recently introduced method [S.-C. Park. J. Korean Phys. Soc. 62, 469 (2013), 10.3938/jkps.62.469]. For small diffusion rate (d ≤0.5 ), the leading corrections-to-scaling term is found to be ˜t-0.15, whereas for large diffusion rate (d =0.95 ) it is found to be ˜t-0.5. After finding the strength of corrections to scaling, effective exponents are systematically analyzed to conclude that the value of critical decay exponent δ is 0.173 (3 ) irrespective of d . This value should be compared with the critical decay exponent of the directed percolation, 0.1595. In addition, we study two types of crossover. At d =0 , the phase boundary is discontinuous and the crossover from the pair contact process to the PCPD is found to be described by the crossover exponent ϕ =2.6 (1 ) . We claim that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP. At d =1 , the crossover from the mean field PCPD to the PCPD is described by ϕ =2 which is argued to be exact.

Critical dynamic approach to stationary states in complex systems

NASA Astrophysics Data System (ADS)

Rozenfeld, A. F.; Laneri, K.; Albano, E. V.

2007-04-01

A dynamic scaling Ansatz for the approach to stationary states in complex systems is proposed and tested by means of extensive simulations applied to both the Bak-Sneppen (BS) model, which exhibits robust Self-Organised Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway, whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations such that ρ(t=0) →0, one observes an initial increase of the density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively; ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS and GOL models, respectively. It is also shown that the temporal autocorrelation decays with exponents Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model. By using these dynamically determined critical exponents and suitable scaling relationships, we also obtain the dynamic exponents z = 2.10(5) (z = 2.10(5)) for the BS (GOL) model. Based on this evidence we conclude that the dynamic approach to stationary states of the investigated models can be described by suitable power-law functions of time with well-defined exponents.

Percolation of the site random-cluster model by Monte Carlo method

NASA Astrophysics Data System (ADS)

Wang, Songsong; Zhang, Wanzhou; Ding, Chengxiang

2015-08-01

We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability Re, the percolating cluster density P∞, and the magnetic susceptibility per site χp, as well as two exponents, such as the thermal exponent yt and the fractal dimension yh of the percolating cluster. We find that for different exponents of cluster weight q =1.5 , 2, 2.5 , 3, 3.5 , and 4, the numerical estimation of the exponents yt and yh are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identical. For larger values of q , we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.

Optical Study of the Critical Behaviour of Pure Fluids and Binary Mixtures.

NASA Astrophysics Data System (ADS)

Narger, Ulrike

1990-01-01

Optical techniques were used to study the critical behaviour of the pure fluids CHF_3, CClF_3 and Xe, and binary mixtures He-Xe and nicotine + water. We find that for all these substances, the order parameter is described by a power law in the reduced temperature t = (T _{c} - T)/T_{c} with a leading exponent beta = 0.327 +/- 0.002. Also, we determine the first correction to scaling exponent to be Delta = 0.43 +/- 0.02 for the pure fluids and Delta = 0.50 +/- 0.02 for the He-Xe system. The coexistence curve diameter in CHF _3 and CClF_3 exhibits a deviation from recti-linear diameter, in agreement with a modern theory which interprets this behaviour as resulting from three-body effects. In contrast, no such deviation is observed in Xe where, according to that theory, it should be more pronounced than in other substances. In the polar fluid CHF_3, the order parameter, isothermal compressibility and the chemical potential along the critical isotherm were simultaneously measured in the same experiment in an effort to ensure self-consistency of the results. From the data, two amplitude ratios which are predicted to be universal are determined: Gamma_sp{0}{+} /Gamma_sp{0}{ -} = 4.8 +/- 0.6 and D_0 Gamma_sp{0}{+ } B_sp{0}{delta-1} = 1.66 +/- 0.14. In the binary liquid system nicotine + water, the diffusivity was measured both by light scattering and by interferometry. The results agree qualitatively, but differ by a factor of ~2. From the light scattering data, the critical exponent of the viscosity is found to be z_{eta } = 0.044 +/- 0.008. The interferometric experiments on Xe and He-Xe furnish a direct way to measure the effects of wetting: From the data, the exponent of the surface tension is found to be n = 1.24 +/- 0.06. The similarity of the order parameter and compressibility in Xe and a He-Xe mixture containing 5% He indicate that the phase transition in this He-Xe mixture is of the liquid -gas type rather than the binary liquid type.

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Petrovic, C.

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE PAGES

Liu, Yu; Petrovic, C.

2017-10-09

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

NASA Astrophysics Data System (ADS)

Odavić, Jovan; Mali, Petar; Tekić, Jasmina; Pantić, Milan; Pavkov-Hrvojević, Milica

2017-06-01

Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middleton's no passing rule.

Superfluid-insulator transition in a disordered two-dimensional quantum rotor model with random on-site interactions

NASA Astrophysics Data System (ADS)

An, Taeyang; Cha, Min-Chul

2013-03-01

We study the superfluid-insulator quantum phase transition in a disordered two-dimensional quantum rotor model with random on-site interactions in the presence of particle-hole symmetry. Via worm-algorithm Monte Carlo calculations of superfluid density and compressibility, we find the dynamical critical exponent z ~ 1 . 13 (2) and the correlation length critical exponent 1 / ν ~ 1 . 1 (1) . These exponents suggest that the insulating phase is a incompressible Mott glass rather than a Bose glass.

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

NASA Astrophysics Data System (ADS)

Li, Liang-Sheng

2016-12-01

We explore the tricritical points and the critical lines of both Blume-Emery-Grifnths and Ising model within long-range interactions in the microcanonical ensemble. For K = K MTP , the tricritical exponents take the values β = 1/4, 1 = γ- ≠ γ+ = 1/2 and 0 = α- ≠ α+ = -1/2, which disagree with classical (mean held) values. When K > K MTP , the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K CTP ), where the values of the critical expoents become β = 1/2, 1 = γ- ≠ γ+ = 2 and 0 = α- ≠ α+ = 1. Supported by the National Natural Science Foundation of China under Grant No. 11104032

The susceptibility critical exponent for a nonaqueous ionic binary mixture near a consolute point

NASA Technical Reports Server (NTRS)

Zhang, Kai C.; Briggs, Matthew E.; Gammon, Robert W.; Levelt Sengers, J. M. H.

1992-01-01

We report turbidity measurements of a nonaqueous ionic solution of triethyl n-hexylammonium triethyl n-hexylboride in diphenyl ether. A classical susceptibility critical exponent gamma = 1.01 +/- 0.01 is obtained over the reduced temperature range t between values of 0.1 and 0.0001. The best fits of the sample transmission had a standard deviation of 0.39 percent over this range. Ising and spherical model critical exponents are firmly excluded. The correlation length amplitude xi sub 0 from fitting is 1.0 +/- 0.2 nm which is much larger than values found in neutral fluids and some aqueous binary mixtures.

Anisotropic Weyl symmetry and cosmology

NASA Astrophysics Data System (ADS)

Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu

2010-11-01

We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Hořava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent z. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for z = -3. We also include the cosmological fluid and show that it can preserve the anisotropic Weyl invariance if the equation of state satisfies P = zρ/3. Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl (EHaW) action including the cosmological fluid, both with or without anisotropic Weyl invariance. The correlation of the critical exponent z and the equation of state parameter bar omega provides a new perspective of the cosmology. It is also shown that the EHaW action admits a late time accelerating universe for an arbitrary value of z when the anisotropic conformal invariance is broken, and the anisotropic conformal scalar field is interpreted as a possible source of dark energy.

Dynamic scaling in natural swarms

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Conti, Daniele; Creato, Chiara; Del Castello, Lorenzo; Giardina, Irene; Grigera, Tomas S.; Melillo, Stefania; Parisi, Leonardo; Viale, Massimiliano

2017-09-01

Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ~ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ~ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

Engineering Surface Critical Behavior of (2 +1 )-Dimensional O(3) Quantum Critical Points

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Zhang, Long; Guo, Wenan

2018-06-01

Surface critical behavior (SCB) refers to the singularities of physical quantities on the surface at the bulk phase transition. It is closely related to and even richer than the bulk critical behavior. In this work, we show that three types of SCB universality are realized in the dimerized Heisenberg models at the (2 +1 )-dimensional O(3) quantum critical points by engineering the surface configurations. The ordinary transition happens if the surface is gapped in the bulk disordered phase, while the gapless surface state generally leads to the multicritical special transition, even though the latter is precluded in classical phase transitions because the surface is in the lower critical dimension. An extraordinary transition is induced by the ferrimagnetic order on the surface of the staggered Heisenberg model, in which the surface critical exponents violate the results of the scaling theory and thus seriously challenge our current understanding of extraordinary transitions.

A Second-Order Phase Transition as a Limit of the First-Order Phase Transitions —Coherent Anomalies and Critical Phenomena in the Potts Models—

NASA Astrophysics Data System (ADS)

Katori, Makoto

1988-12-01

A new scheme of the coherent-anomaly method (CAM) is proposed to study critical phenomena in the models for which a mean-field description gives spurious first-order phase transition. A canonical series of mean-field-type approximations are constructed so that the spurious discontinuity should vanish asymptotically as the approximate critical temperature approachs the true value. The true value of the critical exponents β and γ are related to the coherent-anomaly exponents defined among the classical approximations. The formulation is demonstrated in the two-dimensional q-state Potts models for q{=}3 and 4. The result shows that the present method enables us to estimate the critical exponents with high accuracy by using the date of the cluster-mean-field approximations.

On universality of scaling law describing roughness of triple line.

PubMed

Bormashenko, Edward; Musin, Albina; Whyman, Gene; Barkay, Zahava; Zinigrad, Michael

2015-01-01

The fine structure of the three-phase (triple) line was studied for different liquids, various topographies of micro-rough substrates and various wetting regimes. Wetting of porous and pillar-based micro-scaled polymer surfaces was investigated. The triple line was visualized with the environmental scanning electron microscope and scanning electron microscope for the "frozen" triple lines. The value of the roughness exponent ζ for water (ice)/rough polymer systems was located within 0.55-0.63. For epoxy glue/rough polymer systems somewhat lower values of the exponent, 0.42 < ζ < 0.54, were established. The obtained values of ζ were close for the Cassie and Wenzel wetting regimes, different liquids, and different substrates' topographies. Thus, the above values of the exponent are to a great extent universal. The switch of the exponent, when the roughness size approaches to the correlation length of the defects, is also universal.

Finite-size scaling of survival probability in branching processes

NASA Astrophysics Data System (ADS)

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Álvaro

2015-04-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We derive analytically the existence of finite-size scaling for the survival probability as a function of the control parameter and the maximum number of generations, obtaining the critical exponents as well as the exact scaling function, which is G (y ) =2 y ey /(ey-1 ) , with y the rescaled distance to the critical point. Our findings are valid for any branching process of the Galton-Watson type, independently of the distribution of the number of offspring, provided its variance is finite. This proves the universal behavior of the finite-size effects in branching processes, including the universality of the metric factors. The direct relation to mean-field percolation is also discussed.

Measurements of the magnetic-field-tuned conductivity of disordered two-dimensional Mo43Ge57 and InOx superconducting films: evidence for a universal minimum superfluid response.

PubMed

Misra, S; Urban, L; Kim, M; Sambandamurthy, G; Yazdani, A

2013-01-18

Our measurements of the low frequency ac conductivity in strongly disordered two-dimensional films near the magnetic-field-tuned superconductor-to-insulator transition show a sudden drop in the phase stiffness of superconducting order with either increased temperature or magnetic field. Surprisingly, for two different material systems, the abrupt drop in the superfluid density in a magnetic field has the same universal value as that expected for a Berezinskii-Kosterlitz-Thouless transition in a zero magnetic field. The characteristic temperature at which phase stiffness is suddenly lost can be tuned to zero at a critical magnetic field, following a power-law behavior with a critical exponent consistent with that obtained in previous dc transport studies on the dissipative side of the transition.

Precise calculation of a bond percolation transition and survival rates of nodes in a complex network.

PubMed

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.

Size and density avalanche scaling near jamming.

PubMed

Arévalo, Roberto; Ciamarra, Massimo Pica

2014-04-28

The current microscopic picture of plasticity in amorphous materials assumes local failure events to produce displacement fields complying with linear elasticity. Indeed, the flow properties of nonaffine systems, such as foams, emulsions and granular materials close to jamming, that produce a fluctuating displacement field when failing, are still controversial. Here we show, via a thorough numerical investigation of jammed materials, that nonaffinity induces a critical scaling of the flow properties dictated by the distance to the jamming point. We rationalize this critical behavior by introducing a new universal jamming exponent and hyperscaling relationships, and we use these results to describe the volume fraction dependence of the friction coefficient.

Quantum fluctuations and the closing of the Coulomb gap in a correlated insulator.

PubMed

Roy, A S; Hoekstra, A F Th; Rosenbaum, T F; Griessen, R

2002-12-30

The "switchable mirror" yttrium hydride is one of the few strongly correlated systems with a continuous Mott-Hubbard metal-insulator transition. We systematically map out the low temperature electrical transport from deep in the insulator to the quantum critical point using persistent photoconductivity as a drive parameter. Both activated hopping over a Coulomb gap and power-law quantum fluctuations must be included to describe the data. Collapse of the data onto a universal curve within a dynamical scaling framework (with corrections) requires znu=6.0+/-0.5, where nu and z are the static and dynamical critical exponents, respectively.

Critical behavior of modulus of gel

NASA Astrophysics Data System (ADS)

Tokita, Masayuki; Niki, Ryoya; Hikichi, Kunio

1985-09-01

The critical behavior of the shear modulus of casein gel is studied. The shear modulus of casein gel scales with the conductivity exponent in the immediate vicinity of the sol-gel transition point. The asymptotic behavior of the modulus in the region far above the transition point is governed by a different exponent which is much larger than the conductivity exponent. These results are explainable by the crossover behavior of the percolation process. This study shows that the gelation of the casein micelle solution is a realization of the percolation process.

Critical behavior of the contact process on small-world networks

NASA Astrophysics Data System (ADS)

Ferreira, Ronan S.; Ferreira, Silvio C.

2013-11-01

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering ( p → 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Solar potential scaling and the urban road network topology

NASA Astrophysics Data System (ADS)

Najem, Sara

2017-01-01

We explore the scaling of cities' solar potentials with their number of buildings and reveal a latent dependence between the solar potential and the length of the corresponding city's road network. This scaling is shown to be valid at the grid and block levels and is attributed to a common street length distribution. Additionally, we compute the buildings' solar potential correlation function and length in order to determine the set of critical exponents typifying the urban solar potential universality class.

Entanglement entropies and fermion signs of critical metals

NASA Astrophysics Data System (ADS)

Kaplis, N.; Krüger, F.; Zaanen, J.

2017-04-01

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently has it been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wave-function Ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wave functions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces, a representation of the fermion sign structure in many-particle configurations space, show fractal behavior up to a length scale ξ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on ξ , the number of fermions and the exponent of the backflow. For the same wave functions we numerically calculate the second Rényi entanglement entropy S2. Our results show a crossover from volume scaling, S2˜ℓθ (θ =2 in d =2 dimensions), to the characteristic Fermi-liquid behavior S2˜ℓ lnℓ on scales larger than ξ . We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure.

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

NASA Astrophysics Data System (ADS)

Lepori, L.; Vodola, D.; Pupillo, G.; Gori, G.; Trombettoni, A.

2016-11-01

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent α. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action SD, found in the short-range Ising universality class, and an "anomalous" CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for α > 2, while for α < 2 it dominates and determines the breakdown of the CS. Out of criticality SAN breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite α. As α increases such ELI breakdown becomes less and less pronounced and in the short-range limit α → ∞ the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for α < 1. Finally we show that at every finite α the critical exponents, defined as for the short-range (α → ∞) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of α where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (SD) is present for 1 < α < 2 (for α > 2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken.

Spin chirality and polarised neutron scattering

NASA Astrophysics Data System (ADS)

Plakhty, V. P.; Maleyev, S. V.; Kulda, J.; Visser, E. D.; Wosnitza, J.; Moskvin, E. V.; Brückel, Th.; Kremer, R. K.

2001-03-01

Possibilities of polarised neutrons in studies of chiral criticality are discussed. The critical exponents β C of the average chirality below TN, as well as φ C=β C+γ C and, therefore, γ C of the chiral susceptibility above TN are determined for a XY triangular lattice antiferromagnet (TLA) CsMnBr3: β C=0.44(2) , γ C=0.84(7) . The critical behaviour of the chirality that orders at TN with a relative precision of 5×10 -4 proves that the phase transition belongs to a new chiral universality class. For the TLA CsNiCl 3 ( S=1) we found in the XY region ( B=3 T) φ C=1.24(7) in agreement with the Monte-Carlo value φ C=1.22(6) for the chiral universality class. In the easy-axis region at B=1 T, φ C=0.54(4) , and the Haldane excitations are observed in the polarisation-dependent inelastic cross section above TN. The helimagnet holmium exhibits a different chiral criticality with φ C=1.56(5) , essentially higher than for TLAs.

X-ray scattering study of the spin-Peierls phase transition

NASA Astrophysics Data System (ADS)

Lumsden, Mark Douglas

1999-11-01

Scattering techniques are an essential tool in the experimental study of properties in the vicinity of a critical phase transition. Such techniques have been applied to the study of the spin-Peierls transition in pure and doped samples of CuGeO3 and in the organic compound MEM(TCNQ) 2. The spin-Peierls phase transition occurs in one-dimensional S = 1/2 Heisenberg spin chains with short-range, antiferromagnetic interactions. Such a system is unstable against a dimerization of the chains with the subsequent appearance of a gap in the magnetic excitation spectrum. Such a gap acts to lower the magnetic energy in the system and, in the presence of coupling with the lattice, causes a phase transition to a dimerized, spin-Peierls, state. High temperature stability measurements of the order parameter associated with this transition in the inorganic compound CuGeO3 indicate a continuous phase transition at a temperature of 14.05 K with a corresponding critical exponent beta of 0.345 +/- 0.03. This value is in agreement with conventional 3D universality and in closest agreement with 3D XY behaviour. We also observe a narrow asymptotic critical region which is largely responsible for the inconsistency in previously reported results. High resolution measurements of relative lattice constant changes, performed using a novel approach, indicate spontaneous strains which scale with the square of the order parameter expect near the transition temperature where differences are observed. Similar order parameter measurements were performed on samples of CuGeO 3 doped with Zn, Si, and Cd. For the case of Zn and Si doping, we obtain and exponent beta consistent with that for the pure material. Measurements on two Cd doped samples indicate results which clearly deviate from that observed in pure CuGeO3 with an exponent beta of about 0.5 consistent with mean field behaviour. We explain this change in behaviour as resulting from local strains induced by the presence of the much larger Cd2+ dopant ion. Relative lattice constant measurements indicate spontaneous strains which scale with the square of the order parameter for the doped samples as was the case for pure CuGeO3. X-ray scattering measurements of both the order parameter and critical scattering in the vicinity of the transition temperature have been performed for the organic spin-Peierls compound MEM(TCNQ)2. Order parameter measurements indicate a value of the exponent beta of 0.35 +/- 0.06 consistent with 3D universality, as was observed in the inorganic spin-Peierls material CuGeO3, and inconsistent with previous measurements which suggested mean-field behaviour. Critical scattering measurements suggest a lineshape not described by a traditional Ornstein-Zernike, Lorentzian, form but well described by a Lorentzian with a varying power or a Lorentzian+Lorentzian 2. The latter form is reminiscent of recent x-ray scattering measurements of critical phenomena associated with structural phase transitions in perovskites or with magnetic x-ray scattering measurements on Ho, Tb, and some U-based compounds. Differences between this and previous measurements are discussed.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Dashti-Naserabadi, H.; Mohammadzadeh, H.

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature Tc the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc the model has some aspects compatible with the 2D BTW model (e.g., the 1 /log(L ) -dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1 /L -dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

NASA Astrophysics Data System (ADS)

Maliborski, Maciej; Rinne, Oliver

2018-02-01

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

Validating the operational bias and hypothesis of universal exponent in landslide frequency-area distribution.

PubMed

Huang, Jr-Chuan; Lee, Tsung-Yu; Teng, Tse-Yang; Chen, Yi-Chin; Huang, Cho-Ying; Lee, Cheing-Tung

2014-01-01

The exponent decay in landslide frequency-area distribution is widely used for assessing the consequences of landslides and with some studies arguing that the slope of the exponent decay is universal and independent of mechanisms and environmental settings. However, the documented exponent slopes are diverse and hence data processing is hypothesized for this inconsistency. An elaborated statistical experiment and two actual landslide inventories were used here to demonstrate the influences of the data processing on the determination of the exponent. Seven categories with different landslide numbers were generated from the predefined inverse-gamma distribution and then analyzed by three data processing procedures (logarithmic binning, LB, normalized logarithmic binning, NLB and cumulative distribution function, CDF). Five different bin widths were also considered while applying LB and NLB. Following that, the maximum likelihood estimation was used to estimate the exponent slopes. The results showed that the exponents estimated by CDF were unbiased while LB and NLB performed poorly. Two binning-based methods led to considerable biases that increased with the increase of landslide number and bin width. The standard deviations of the estimated exponents were dependent not just on the landslide number but also on binning method and bin width. Both extremely few and plentiful landslide numbers reduced the confidence of the estimated exponents, which could be attributed to limited landslide numbers and considerable operational bias, respectively. The diverse documented exponents in literature should therefore be adjusted accordingly. Our study strongly suggests that the considerable bias due to data processing and the data quality should be constrained in order to advance the understanding of landslide processes.

Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts; Ivanova, E. V.; Kompaniets, M. V.; Vorobyeva, S. Ye

2018-04-01

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent z of model A at 4-loop level, where our method allows one to reduce the number of integrals from 66 to 17. The way of constructing the integrand in a Feynman representation of such diagrams is discussed. Integrals were estimated numerically with a sector decomposition technique.

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network

PubMed Central

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition. PMID:25885791

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

NASA Astrophysics Data System (ADS)

Doggen, Elmer V. H.; Lemarié, Gabriel; Capponi, Sylvain; Laflorencie, Nicolas

2017-11-01

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter Kc takes its universal Giamarchi-Schulz value Kc=3 /2 . Conversely, a nonuniversal Kc>3 /2 emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent α .

Threshold of coexistence and critical behavior of a predator-prey stochastic model in a fractal landscape

NASA Astrophysics Data System (ADS)

Argolo, C.; Barros, P.; Tomé, T.; Arashiro, E.; Gleria, Iram; Lyra, M. L.

2016-08-01

We investigate a stochastic lattice model describing a predator-prey system in a fractal scale-free landscape, mimicked by the fractal Sierpinski carpet. We determine the threshold of species coexistence, that is, the critical phase boundary related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. We show that the predators must live longer in order to persist in a fractal habitat. We further performed a finite-size scaling analysis in the vicinity of the absorbing-state phase transition to compute a set of stationary and dynamical critical exponents. Our results indicate that the transition belongs to the directed percolation universality class exhibited by the usual contact process model on the same fractal landscape.

Product-sum universality and Rushbrooke inequality in explosive percolation

NASA Astrophysics Data System (ADS)

Sabbir, M. M. H.; Hassan, M. K.

2018-05-01

We study explosive percolation (EP) on an Erdös-Rényi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition; now it is well accepted as a probabilistic model for thermal continuous phase transition (CPT). However, no model for CPT is complete unless we know how to relate its observable quantities with those of thermal CPT. To this end, we define entropy and specific heat, redefine susceptibility, and show that they behave exactly like their thermal counterparts. We obtain the critical exponents ν ,α ,β , and γ numerically and find that both PR and SR belong to the same universality class and obey Rushbrooke inequality.

Two-Dimensional SIR Epidemics with Long Range Infection

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2013-10-01

We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law p( x)˜| x|- σ-2 for the probability that a site can infect another site a distance vector x apart. As in I we present detailed results for the critical case, for the supercritical case with σ=2, and for the supercritical case with 0< σ<2. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For σ=2 we find generic power laws with σ-dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on σ in the regime 0< σ<2, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for σ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder et al. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.

Absorbing states in a catalysis model with anti-Arrhenius behavior.

PubMed

de Andrade, M F; Figueiredo, W

2012-04-28

We study a model of heterogeneous catalysis with competitive reactions between two monomers A and B. We assume that reactions are dependent on temperature and follow an anti-Arrhenius mechanism. In this model, a monomer A can react with a nearest neighbor monomer A or B, however, reactions between monomers of type B are not allowed. We assume attractive interactions between nearest neighbor monomers as well as between monomers and the catalyst. Through mean-field calculations, at the level of site and pair approximations, and extensive Monte Carlo simulations, we determine the phase diagram of the model in the plane y(A) versus temperature, where y(A) is the probability that a monomer A reaches the catalyst. The model exhibits absorbing and active phases separated by lines of continuous phase transitions. We calculate the static, dynamic, and spreading exponents of the model, and despite the absorbing state be represented by many different microscopic configurations, the model belongs to the directed percolation universality class in two dimensions. Both reaction mechanisms, Arrhenius and anti-Arrhenius, give the same set of critical exponents and do not change the nature of the universality class of the catalytic models.

Critical exponents of extremal Kerr perturbations

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.; Zimmerman, Peter

2018-05-01

We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero.

Beyond Critical Exponents in Neuronal Avalanches

NASA Astrophysics Data System (ADS)

Friedman, Nir; Butler, Tom; Deville, Robert; Beggs, John; Dahmen, Karin

2011-03-01

Neurons form a complex network in the brain, where they interact with one another by firing electrical signals. Neurons firing can trigger other neurons to fire, potentially causing avalanches of activity in the network. In many cases these avalanches have been found to be scale independent, similar to critical phenomena in diverse systems such as magnets and earthquakes. We discuss models for neuronal activity that allow for the extraction of testable, statistical predictions. We compare these models to experimental results, and go beyond critical exponents.

Self-organized criticality in a network of economic agents with finite consumption

NASA Astrophysics Data System (ADS)

da Cruz, João P.; Lind, Pedro G.

2012-02-01

We introduce a minimal agent model to explain the emergence of heavy-tailed return distributions as a result of self-organized criticality. The model assumes that agents trade their economic outputs with each other composing a complex network of agents and connections. Further, the incoming degree of an agent is proportional to the demand on its goods, while its outgoing degree is proportional to the supply. The model considers a collection of economic agents which are attracted to establish connections among them to make an exchange at a price formed by supply and demand. With our model we are able to reproduce the evolution of the return of macroscopic quantities (indices) and to correctly retrieve the non-trivial exponent value characterizing the amplitude of drops in several indices in financial markets, relating it to the underlying topology of connections. The distribution of drops in empirical data is obtained by counting the number of successive time-steps for which a decrease in the index value is observed. All eight financial indexes show an exponent m˜5/2. Finally, we present mean-field calculations of the critical exponents, and of the scaling relation m=3/2 γ-1 between the exponent m for the distribution of drops and the topological exponent γ for the degree distribution.

Mean-field behavior as a result of noisy local dynamics in self-organized criticality: Neuroscience implications

NASA Astrophysics Data System (ADS)

Moosavi, S. Amin; Montakhab, Afshin

2014-05-01

Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (nonconservative) local dynamics on the critical behavior of a sandpile model which can be taken to mimic the dynamics of neuronal avalanches. We find that despite the fact that noise breaks the strict local conservation required to attain criticality, our system exhibits true criticality for a wide range of noise in various dimensions, given that conservation is respected on the average. Although the system remains critical, exhibiting finite-size scaling, the value of critical exponents change depending on the intensity of local noise. Interestingly, for a sufficiently strong noise level, the critical exponents approach and saturate at their mean-field values, consistent with empirical measurements of neuronal avalanches. This is confirmed for both two and three dimensional models. However, the addition of noise does not affect the exponents at the upper critical dimension (D =4). In addition to an extensive finite-size scaling analysis of our systems, we also employ a useful time-series analysis method to establish true criticality of noisy systems. Finally, we discuss the implications of our work in neuroscience as well as some implications for the general phenomena of criticality in nonequilibrium systems.

Validating the Operational Bias and Hypothesis of Universal Exponent in Landslide Frequency-Area Distribution

PubMed Central

Huang, Jr-Chuan; Lee, Tsung-Yu; Teng, Tse-Yang; Chen, Yi-Chin; Huang, Cho-Ying; Lee, Cheing-Tung

2014-01-01

The exponent decay in landslide frequency-area distribution is widely used for assessing the consequences of landslides and with some studies arguing that the slope of the exponent decay is universal and independent of mechanisms and environmental settings. However, the documented exponent slopes are diverse and hence data processing is hypothesized for this inconsistency. An elaborated statistical experiment and two actual landslide inventories were used here to demonstrate the influences of the data processing on the determination of the exponent. Seven categories with different landslide numbers were generated from the predefined inverse-gamma distribution and then analyzed by three data processing procedures (logarithmic binning, LB, normalized logarithmic binning, NLB and cumulative distribution function, CDF). Five different bin widths were also considered while applying LB and NLB. Following that, the maximum likelihood estimation was used to estimate the exponent slopes. The results showed that the exponents estimated by CDF were unbiased while LB and NLB performed poorly. Two binning-based methods led to considerable biases that increased with the increase of landslide number and bin width. The standard deviations of the estimated exponents were dependent not just on the landslide number but also on binning method and bin width. Both extremely few and plentiful landslide numbers reduced the confidence of the estimated exponents, which could be attributed to limited landslide numbers and considerable operational bias, respectively. The diverse documented exponents in literature should therefore be adjusted accordingly. Our study strongly suggests that the considerable bias due to data processing and the data quality should be constrained in order to advance the understanding of landslide processes. PMID:24852019

Pressure-induced quantum phase transition in the quantum antiferromagnet CsFeCl3

NASA Astrophysics Data System (ADS)

Hayashida, Shohei; Zaharko, Oksana; Kurita, Nobuyuki; Tanaka, Hidekazu; Hagihala, Masato; Soda, Minoru; Itoh, Shinichi; Uwatoko, Yoshiya; Masuda, Takatsugu

2018-04-01

We have studied the pressure-induced quantum phase transition in the singlet-ground-state antiferromagnet CsFeCl3. Neutron diffraction experiments under pressure evidence the magnetic long-range order at low temperatures. Magnetic structure analysis reveals a 120∘ structure with a propagation vector of kmag=(1 /3 ,1 /3 ,0 ) . The estimated critical exponent of the order parameter suggests that CsFeCl3 belongs to the universality class of U (1 ) ×Z2 symmetry which is expected to realize the chiral liquid state.

Demonstration of the Kibble-Zurek mechanism in a non-equilibrium phase transition

NASA Astrophysics Data System (ADS)

Patil, Yogesh S.; Cheung, Hil F. H.; Date, Aditya G.; Vengalattore, Mukund

2017-04-01

We describe the experimental realization of a driven-dissipative phase transition (DPT) in a mechanical parametric amplifier and demonstrate key signatures of a critical point in the system, where the susceptibilities and relaxation time scales diverge and coincide with the spontaneous breaking of symmetry and the emergence of macroscopic order. While these observations are reminiscent of equilibrium phase transitions, it is presently an open question whether such DPTs are amenable to the conventional Landau-Ginsburg-Wilson paradigm that relies on concepts of scale invariance and universality - Indeed, recent theoretical work has predicted that DPTs can exhibit phenomenology that departs from these conventional paradigms. By quenching the system past the critical point, we measure the dynamics of the emergent ordered phase and its departure from adiabaticity, and find that our measurements are in excellent agreement with the Kibble-Zurek hypothesis. In addition to validating the KZ mechanism in a DPT for the first time, we also uniquely show that the measured critical exponents accurately reflect the interplay between the intrinsic coherent dynamics and the environmental correlations, with a clear departure from mean field exponents in the case of non-Markovian system-bath interactions. We also discuss how the techniques of reservoir engineering and the imposition of artificial environmental correlations can result in the stabilization of novel many-body quantum phases and exotic non-equilibrium states of matter.

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

NASA Astrophysics Data System (ADS)

Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song

2016-10-01

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384

Turbidity of a Binary Fluid Mixture: Determining Eta

NASA Technical Reports Server (NTRS)

Jacobs, Donald T.

1996-01-01

A ground based (1-g) experiment is in progress that will measure the turbidity of a density-matched, binary fluid mixture extremely close to its liquid-liquid critical point. By covering the range of reduced temperatures t equivalent to (T-T(sub c)) / T(sub c) from 10(exp -8) to 10(exp -2), the turbidity measurements will allow the critical exponent eta to be determined. No experiment has precisely determined a value of the critical exponent eta, yet its value is significant to theorists in critical phenomena. Relatively simple critical phenomena, as in the liquid-liquid system studied here, serve as model systems for more complex systems near a critical point.

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Lyapunov exponent and criticality in the Hamiltonian mean field model

NASA Astrophysics Data System (ADS)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

Endogenous and exogenous dynamics in the fluctuations of capital fluxes. An empirical analysis of the Chinese stock market

NASA Astrophysics Data System (ADS)

Jiang, Z.-Q.; Guo, L.; Zhou, W.-X.

2007-06-01

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σexo / σendo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent Hi increase in logarithmic form with the time scale Δt and the mean traded value per minute , respectively. We find that the scaling exponent αendo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.

Universality of magnetic-field-induced Bose-Einstein condensation of magnons

NASA Astrophysics Data System (ADS)

Shirasawa, Kazuki; Kurita, Nobuyuki; Tanaka, Hidekazu

2017-10-01

CsFeBr3 is an S =1 hexagonal antiferromagnet that has a singlet ground state owing to its large easy-plane single-ion anisotropy. The critical behavior of the magnetic-field-induced phase transition for a magnetic field parallel to the c axis, which can be described by the Bose-Einstein condensation (BEC) of magnons under the U (1 ) symmetry, was investigated via magnetization and specific heat measurements down to 0.1 K. For the specific heat measurement, we have developed a method of effectively suppressing the torque acting on a sample with strong anisotropy that uses the spin dimer compound Ba2CoSi2O6Cl2 with large and anisotropic Van Vleck paramagnetism. The temperature dependence of the transition field Hc(T ) was found to follow the power-law Hc(T ) -Hc∝Tϕ with a critical exponent of ϕ =1.50 ±0.02 and critical field of Hc=2.60 T . This result verifies the universality of the three-dimensional BEC of magnons described by ϕBEC=3 /2 .

Adsorption of a single polymer chain on a surface: Effects of the potential range

NASA Astrophysics Data System (ADS)

Klushin, Leonid I.; Polotsky, Alexey A.; Hsu, Hsiao-Ping; Markelov, Denis A.; Binder, Kurt; Skvortsov, Alexander M.

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value Uc corresponding to the adsorption transition scales as W-1/ν, where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory Uc≈((π2)/(24))(W+1/2)-2 and in the best-fit equation for the MC simulation data Uc=0.585(W+1/2)-5/3. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NUc,U/Uc). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N˜5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent ϕeff(N). Strong corrections to scaling of order N-0.5 are observed, and the extrapolated value ϕ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of ϕeff(N) were identified as the asymptotic value for the crossover exponent.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

Quantum Quench Dynamics

NASA Astrophysics Data System (ADS)

Mitra, Aditi

2018-03-01

Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum quenches is reviewed. Quenches in interacting one-dimensional systems as well as systems in higher spatial dimensions are covered. The appearance of nontrivial steady states following a quench in exactly solvable models is discussed, and the stability of these states to perturbations is described. Proper conserving approximations needed to capture the onset of thermalization at long times are outlined. The appearance of universal scaling for quenches near critical points and the role of the renormalization group in capturing the transient regime are reviewed. Finally, the effect of quenches near critical points on the dynamics of entanglement entropy and entanglement statistics is discussed. The extraction of critical exponents from the entanglement statistics is outlined.

Adiabatic physics of an exchange-coupled spin-dimer system: Magnetocaloric effect, zero-point fluctuations, and possible two-dimensional universal behavior

DOE PAGES

Brambleby, J.; Goddard, P. A.; Singleton, John; ...

2017-01-05

We present the magnetic and thermal properties of the bosonic-superfluid phase in a spin-dimer network using both quasistatic and rapidly changing pulsed magnetic fields. The entropy derived from a heat-capacity study reveals that the pulsed-field measurements are strongly adiabatic in nature and are responsible for the onset of a significant magnetocaloric effect (MCE). In contrast to previous predictions we show that the MCE is not just confined to the critical regions, but occurs for all fields greater than zero at sufficiently low temperatures. We explain the MCE using a model of the thermal occupation of exchange-coupled dimer spin states andmore » highlight that failure to take this effect into account inevitably leads to incorrect interpretations of experimental results. In addition, the heat capacity in our material is suggestive of an extraordinary contribution from zero-point fluctuations and appears to indicate universal behavior with different critical exponents at the two field-induced critical points. Finally, the data at the upper critical point, combined with the layered structure of the system, are consistent with a two-dimensional nature of spin excitations in the system.« less

Finite-size scaling study of the two-dimensional Blume-Capel model

NASA Astrophysics Data System (ADS)

Beale, Paul D.

1986-02-01

The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (Tt=0.610+/-0.005, Dt=1.9655+/-0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.

Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

PubMed

Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

2015-12-01

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

Critical behavior of the contact process in a multiscale network

NASA Astrophysics Data System (ADS)

Ferreira, Silvio C.; Martins, Marcelo L.

2007-09-01

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barabási-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak’s duration, were found. A generalized scaling function involving both regular and SF components was proposed for the quasistationary analysis and the associated critical exponents determined, demonstrating that the CP on this hybrid network and nonvanishing travel rates establishes a new universality class.

Criticality and phase diagram of quantum long-range O(N ) models

NASA Astrophysics Data System (ADS)

Defenu, Nicolò; Trombettoni, Andrea; Ruffo, Stefano

2017-09-01

Several recent experiments in atomic, molecular, and optical systems motivated a huge interest in the study of quantum long-range systems. Our goal in this paper is to present a general description of their critical behavior and phases, devising a treatment valid in d dimensions, with an exponent d +σ for the power-law decay of the couplings in the presence of an O(N ) symmetry. By introducing a convenient ansatz for the effective action, we determine the phase diagram for the N -component quantum rotor model with long-range interactions, with N =1 corresponding to the Ising model. The phase diagram in the σ -d plane shows a nontrivial dependence on σ . As a consequence of the fact that the model is quantum, the correlation functions are anisotropic in the spatial and time coordinates for σ smaller than a critical value, and in this region the isotropy is not restored even at criticality. Results for the correlation length exponent ν , the dynamical critical exponent z , and a comparison with numerical findings for them are presented.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

PubMed Central

Dziarmaga, Jacek; Zurek, Wojciech H.

2014-01-01

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

Characterizing Submonolayer Growth of 6P on Mica: Capture Zone Distributions vs. Growth Exponents and the Role of Hot Precursors

NASA Astrophysics Data System (ADS)

Einstein, T. L.; Morales-Cifuentes, Josue; Pimpinelli, Alberto

2015-03-01

Analyzing capture-zone distributions (CZD) using the generalized Wigner distribution (GWD) has proved a powerful way to access the critical nucleus size i. Of the several systems to which the GWD has been applied, we consider 6P on mica, for which Winkler's group found i ~ 3 . Subsequently they measured the growth exponent α (island density ~Fα , for flux F) of this system and found good scaling but different values at small and large F, which they attributed to DLA and ALA dynamics, but with larger values of i than found from the CZD analysis. We investigate this result in some detail. The third talk of this group describes a new universal relation between α and the characteristic exponent β of the GWD. The second talk reports the results of a proposed model that takes long-known transient ballistic adsorption into account, for the first time in a quantitative way. We find several intermediate scaling regimes, with distinctive values of α and an effective activation energy. One of these, rather than ALA, gives the best fit of the experimental data and a value of i consistent with the CZD analysis. Work at UMD supported by NSF CHE 13-05892.

Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

PubMed

Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael

2011-02-01

This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.

Turbidity of a binary fluid mixture: Determining eta

NASA Technical Reports Server (NTRS)

Jacobs, Donald T.

1994-01-01

A ground based (1-g) experiment is in progress that will measure the turbidity of a density-matched, binary fluid mixture extremely close to the critical point. By covering the range of reduced temperatures t is equivalent to (T-T(sub c))/T(sub c) from 10(exp -8) to 10(exp -2), the turbidity measurements will allow the critical exponent eta to be determined. No experiment has determined a value of the critical exponent eta, yet its value is significant to theorists in critical phenomena. Interpreting the turbidity correctly is important if future NASA flight experiments use turbidity as an indirect measurement of relative temperature in shuttle experiments on critical phenomena in fluids.

Fibonacci family of dynamical universality classes.

PubMed

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M

2015-10-13

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models

NASA Astrophysics Data System (ADS)

Jeong, Hyun-Sik; Ahn, Yongjun; Ahn, Dujin; Niu, Chao; Li, Wei-Jia; Kim, Keun-Young

2018-01-01

We study a relation between the thermal diffusivity ( D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity ( v B ) in strongly correlated systems by using a holographic method. Recently, it was shown that E_i:={D}_{T,i}/({v}{^{B,i}}^2{τ}_L)(i=x,y) is universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for E_i in terms of the critical dynamical exponents z i in each direction, E_i={z}_i/2({z}_i-1) . Furthermore, we find the lower bound of E_i is always 1 /2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy.

Random-fractal Ansatz for the configurations of two-dimensional critical systems

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki

2016-12-01

Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.

Data collapse and critical dynamics in neuronal avalanche data

NASA Astrophysics Data System (ADS)

Butler, Thomas; Friedman, Nir; Dahmen, Karin; Beggs, John; Deville, Lee; Ito, Shinya

2012-02-01

The tasks of information processing, computation, and response to stimuli require neural computation to be remarkably flexible and diverse. To optimally satisfy the demands of neural computation, neuronal networks have been hypothesized to operate near a non-equilibrium critical point. In spite of their importance for neural dynamics, experimental evidence for critical dynamics has been primarily limited to power law statistics that can also emerge from non-critical mechanisms. By tracking the firing of large numbers of synaptically connected cortical neurons and comparing the resulting data to the predictions of critical phenomena, we show that cortical tissues in vitro can function near criticality. Among the most striking predictions of critical dynamics is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function (data collapse). We show for the first time that this prediction is confirmed in neuronal networks. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

PubMed Central

Hoang, Thai M.; Bharath, Hebbe M.; Boguslawski, Matthew J.; Anquez, Martin; Robbins, Bryce A.; Chapman, Michael S.

2016-01-01

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu–Goldstone modes and massive Anderson–Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble–Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition. PMID:27503886

Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions.

PubMed

Bayat, Abolfazl

2017-01-20

The emergence of a diverging length scale in many-body systems at a quantum phase transition implies that total entanglement has to reach its maximum there. In order to fully characterize this, one has to consider multipartite entanglement as, for instance, bipartite entanglement between individual particles fails to signal this effect. However, quantification of multipartite entanglement is very hard, and detecting it may not be possible due to the lack of accessibility to all individual particles. For these reasons it will be more sensible to partition the system into relevant subsystems, each containing a few to many spins, and study entanglement between those constituents as a coarse-grain picture of multipartite entanglement between individual particles. In impurity systems, famously exemplified by two-impurity and two-channel Kondo models, it is natural to divide the system into three parts, namely, impurities and the left and right bulks. By exploiting two tripartite entanglement measures, based on negativity, we show that at impurity quantum phase transitions the tripartite entanglement diverges and shows scaling behavior. While the critical exponents are different for each tripartite entanglement measure, they both provide very similar critical exponents for the two-impurity and the two-channel Kondo models, suggesting that they belong to the same universality class.

Directed Abelian algebras and their application to stochastic models.

PubMed

Alcaraz, F C; Rittenberg, V

2008-10-01

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk.

PubMed

Cheraghalizadeh, J; Najafi, M N; Dashti-Naserabadi, H; Mohammadzadeh, H

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.

Phase and vortex correlations in superconducting Josephson-junction arrays at irrational magnetic frustration.

PubMed

Granato, Enzo

2008-07-11

Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel-tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent nuph, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent nuv, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

NASA Astrophysics Data System (ADS)

Péli, Zoltán; Nagy, Sándor; Sailer, Kornel

2018-02-01

The effect of the O(partial4) terms of the gradient expansion on the anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean 3-dimensional O( N) models with N≥ 2 . Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory is well approximated by the effective average action preserving O( N) symmetry with an accuracy of O(η).

Coherent-Anomaly Method in Critical Phenomena. III.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc* = 2.271 (J/kB), γ=γ' ≃ 1.749, β≃0.131 and δ ≃ 15.1. The specific heat is confirmed to be continuous and to have a logarithmic divergence at the true critical point, i.e., α=α'=0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Theoretical Insight Into the Empirical Tortuosity-Connectivity Factor in the Burdine-Brooks-Corey Water Relative Permeability Model

NASA Astrophysics Data System (ADS)

Ghanbarian, Behzad; Ioannidis, Marios A.; Hunt, Allen G.

2017-12-01

A model commonly applied to the estimation of water relative permeability krw in porous media is the Burdine-Brooks-Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity-connectivity factor is assumed to be a power law function of effective saturation with an exponent (μ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity-connectivity exponent μ to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation-dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of μ in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining μ from the electrical conductivity scaling exponent t, but also highlights limitations of the model.

Three-state Potts model on non-local directed small-world lattices

NASA Astrophysics Data System (ADS)

Ferraz, Carlos Handrey Araujo; Lima, José Luiz Sousa

2017-10-01

In this paper, we study the non-local directed Small-World (NLDSW) disorder effects in the three-state Potts model as a form to capture the essential features shared by real complex systems where non-locality effects play a important role in the behavior of these systems. Using Monte Carlo techniques and finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents in this model. In particular, we investigate the first- to second-order phase transition crossover when NLDSW links are inserted. A cluster-flip algorithm was used to reduce the critical slowing down effect in our simulations. We find that for a NLDSW disorder densities p

Weyl holographic superconductor in the Lifshitz black hole background

NASA Astrophysics Data System (ADS)

Mansoori, S. A. Hosseini; Mirza, B.; Mokhtari, A.; Dezaki, F. Lalehgani; Sherkatghanad, Z.

2016-07-01

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, γ. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters γ and z. Finally, we show numerically that the Weyl coupling parameter γ and the Lifshitz dynamical exponent z together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature ω g /T c .

Finite-time scaling at the Anderson transition for vibrations in solids

NASA Astrophysics Data System (ADS)

Beltukov, Y. M.; Skipetrov, S. E.

2017-11-01

A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame exhibits an Anderson localization transition. To study this transition, we assume that the dynamical matrix of the network is given by a product of a sparse random matrix with real, independent, Gaussian-distributed nonzero entries and its transpose. A finite-time scaling analysis of the system's response to an initial excitation allows us to estimate the critical parameters of the localization transition. The critical exponent is found to be ν =1.57 ±0.02 , in agreement with previous studies of the Anderson transition belonging to the three-dimensional orthogonal universality class.

Non-Abelian Bosonization and Fractional Quantum Hall Transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

A fully satisfying theoretical description for the quantum phase transition between fractional quantum Hall plateaus remains an outstanding problem. Experiments indicate scaling exponents that are not readily obtained in conventional theories. Using insights from duality, we describe a class of quantum critical effective theories that produce qualitatively realistic scaling exponents for the transition. We discuss the implications of our results for the physically-relevant interactions controlling this broad class of quantum critical behavior. Supported by National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1650441.

Fibonacci family of dynamical universality classes

PubMed Central

Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes; Schütz, Gunter M.

2015-01-01

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent z=2, another prominent example is the superdiffusive Kardar−Parisi−Zhang (KPZ) class with z=3/2. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents zα are given by ratios of neighboring Fibonacci numbers, starting with either z1=3/2 (if a KPZ mode exist) or z1=2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean z=(1+5)/2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement. PMID:26424449

On universal procrastination

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-09-01

This paper presents a general stochastic model for procrastination with respect to a deadline. The model establishes a universal procrastination pattern that follows an inverse power-law: if the time remaining to the deadline is r then the response is 1/rε , where ɛ is a positive exponent. The model further establishes that the exponent value ε =1 , which yields the harmonic response 1/r , stands out as special and distinguishable. The theoretical results of the model are shown to be in perfect accord with recent empirical findings.

Progress in Developing a New Field-theoretical Crossover Equation-of-State

NASA Technical Reports Server (NTRS)

Rudnick, Joseph; Barmatz, M.; Zhong, Fang

2003-01-01

A new field-theoretical crossover equation-of-state model is being developed. This model of a liquid-gas critical point provides a bridge between the asymptotic equation-of-state behavior close to the transition, obtained by the Guida and Zinn-Justin parametric model [J. Phys. A: Math. Gen. 31, 8103 (1998)], and the expected mean field behavior farther away. The crossover is based on the beta function for the renormalized fourth-order coupling constant and incorporates the correct crossover exponents and critical amplitude ratios in both regimes. A crossover model is now being developed that is consistent with predictions along the critical isochore and along the coexistence curve of the minimal subtraction renormalization approach developed by Dohm and co-workers and recently applied to the O(1) universality class [Phys. Rev. E, 67, 021106 (2003)]. Experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve near the He-3 critical point are being compared to the predictions of this model. The results of these comparisons will be presented.

Intraspecific variation in the metabolic scaling exponent in ectotherms: testing the effect of latitudinal cline, ontogeny and transgenerational change in the land snail Cornu aspersum.

PubMed

Gaitán-Espitia, Juan Diego; Bruning, Andrea; Mondaca, Fredy; Nespolo, Roberto F

2013-06-01

The strong dependence of metabolic rates on body mass has attracted the interest of ecological physiologists, as it has important implications to many aspects of biology including species variations in body size, the evolution of life history, and the structure and function of biological communities. The great diversity of observed scaling exponents has led some authors to conclude that there is no single universal scaling exponent, but instead it ranges from 2/3 to 1. Most of the telling evidence against the universality of power scaling exponents comes from ontogenetic changes. Nevertheless, there could be other sources of phenotypic variation that influence this allometric relationship at least at the intraspecific level. In order to explore the general concept of the metabolic scaling in terrestrial molluscs we tested the role of several biological and methodological sources of variation on the empirically estimated scaling exponent. Specifically, we measured a proxy of metabolic rate (CO(2) production) in 421 individuals, during three generations, in three different populations. Additionally, we measured this scaling relationship in 208 individuals at five developmental stages. Our results suggest that the metabolic scaling exponent at the intraspecific level does not have a single stationary value, but instead it shows some degree of variation across geographic distribution, transgenerational change and ontogenetic stages. The major differences in the metabolic scaling exponent that we found were at different developmental stages of snails, because ontogeny involves increases in size at different rates, which in turn, generate differential energy demands. Copyright © 2013 Elsevier Inc. All rights reserved.

Revisiting Kawasaki dynamics in one dimension

NASA Astrophysics Data System (ADS)

Grynberg, M. D.

2010-11-01

Critical exponents of the Kawasaki dynamics in the Ising chain are re-examined numerically through the spectrum gap of evolution operators constructed both in spin and domain-wall representations. At low-temperature regimes the latter provides a rapid finite-size convergence to these exponents, which tend to z≃3.11 for instant quenches under ferromagnetic couplings, while approaching to z≃2 in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.

Coherent-Anomaly Method in Critical Phenomena. III. Mean-Field Transfer-Matrix Method in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

1987-11-01

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc*≃2.271 (J/kB), γ{=}γ'≃1.749, β≃0.131 and δ≃15.1. The specific heat is confirmd to be continuous and to have a logarithmic divergence at the true critical point, i.e., α{=}α'{=}0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Three-dimensional magnetic critical behavior in CrI 3

DOE PAGES

Liu, Yu; Petrovic, C.

2018-01-18

CrI 3 is a promising candidate for the van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating of bulk crystals down to single layer. In this work we studied critical properties of bulk CrI 3 single crystals around the paramagnetic to ferromagnetic phase transition. Critical exponents β= 0.260(4) with a critical temperature T c= 60.05(13) K and γ= 1.136(6) with T c= 60.43(4) K are obtained by the Kouvel-Fisher method, whereas δ= 5.32(2) is obtained by a critical isotherm analysis at T c= 60 K. In conclusion, the critical exponents determined in bulk CrI 3more » single crystals suggest a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r)≈r -4:69« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Petrovic, C.

CrI 3 is a promising candidate for the van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating of bulk crystals down to single layer. In this work we studied critical properties of bulk CrI 3 single crystals around the paramagnetic to ferromagnetic phase transition. Critical exponents β= 0.260(4) with a critical temperature T c= 60.05(13) K and γ= 1.136(6) with T c= 60.43(4) K are obtained by the Kouvel-Fisher method, whereas δ= 5.32(2) is obtained by a critical isotherm analysis at T c= 60 K. In conclusion, the critical exponents determined in bulk CrI 3more » single crystals suggest a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r)≈r -4:69« less

Coherent-Anomaly Method in Critical Phenomena. IV.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν·ηi=β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

2011-11-15

We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for noninteracting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudodisorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andre model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the noninteracting quantum critical point of the Aubry-Andre model.

Mean-field Ising crossover and the critical exponents γ, ν, and η for a polymer blend: d-PB/PS studied by small-angle neutron scattering

NASA Astrophysics Data System (ADS)

Janssen, S.; Schwahn, D.; Springer, T.

1992-05-01

The critical behavior of the polymer blend d-PB/PS was investigated by small-angle neutron scattering experiments. 3D Ising behavior was clearly observed with the critical exponents γ=1.26+/-0.01, ν=0.59+/-0.01, and η=0.047+/-0.004. The crossover to mean-field behavior occurs at T*=Tc+5.4 K. This is compared with the results of other experiments and the Landau-Ginzburg criterion. The Q dependence of the structure factor S(Q) follows the Ornstein-Zernike form in both regimes.

Quenched bond randomness: Superfluidity in porous media and the strong violation of universality

NASA Astrophysics Data System (ADS)

Falicov, Alexis; Berker, A. Nihat

1997-04-01

The effects of quenched bond randomness are most readily studied with superfluidity immersed in a porous medium. A lattice model for3He-4He mixtures and incomplete4He fillings in aerogel yields the signature effect of bond randomness, namely the conversion of symmetry-breaking first-order phase transitions into second-order phase transitions, the λ-line reaching zero temperature, and the elimination of non-symmetry-breaking first-order phase transitions. The model recognizes the importance of the connected nature of aerogel randomness and thereby yields superfluidity at very low4He concentrations, a phase separation entirely within the superfluid phase, and the order-parameter contrast between mixtures and incomplete fillings, all in agreement with experiments. The special properties of the helium mixture/aerogel system are distinctly linked to the aerogel properties of connectivity, randomness, and tenuousness, via the additional study of a regularized “jungle-gym” aerogel. Renormalization-group calculations indicate that a strong violation of the empirical universality principle of critical phenomena occurs under quenched bond randomness. It is argued that helium/aerogel critical properties reflect this violation and further experiments are suggested. Renormalization-group analysis also shows that, adjoiningly to the strong universality violation (which hinges on the occurrence or non-occurrence of asymptotic strong coupling—strong randomness under rescaling), there is a new “hyperuniversality” at phase transitions with asymptotic strong coupling—strong randomness behavior, for example assigning the same critical exponents to random- bond tricriticality and random- field criticality.

Are seismic waiting time distributions universal?

NASA Astrophysics Data System (ADS)

Davidsen, Jörn; Goltz, Christian

2004-11-01

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent α ~ 1.1 for intermediate and with exponent γ ~ 0.6 for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a non-trivial way on the geological area under consideration and its size. This is due to the spatial distribution of epicenters which does not form a simple mono-fractal. Yet, the dependence of the waiting time distributions on the threshold magnitude seems to be universal.

Adsorption of a single polymer chain on a surface: effects of the potential range.

PubMed

Klushin, Leonid I; Polotsky, Alexey A; Hsu, Hsiao-Ping; Markelov, Denis A; Binder, Kurt; Skvortsov, Alexander M

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Moessbauer effect: Study of disordered magnetic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Xiao Sha.

1989-01-01

This dissertation describes Moessbauer spectroscopy studies of two chemically disordered binary, crystalline alloys having the composition A{sub 1-x}B{sub x}. Both systems are random 3d Heisenberg ferromagnets. In each case both A and B atoms carry a magnetic moment. The first study concerns a Moessbauer absorber experiment on Fe{sub 1-x} V{sub x}, in which the disorder in the critical region is of the annealed random exchange type. To eliminate the effect of concentration inhomogeneity, the measurement of the critical exponent {beta} was done on the alloy with x = 0.125, where dT{sub C}/dx = 0, yielding {beta} = 0.362(8) over themore » reduced temperature range 1.4 {times} 10{sup {minus}3} < t < 4.88 {times} 10{sup {minus}1}. This result confirms the theoretical prediction that the annealed disorder is irrelevant to critical behavior in this case. As expected the critical exponent {beta} is consistent with the expectation for the 3d Heisenberg model as well as the measured exponent of pure Fe. The second study involves a Moessbauer source experiment on {sup 57} CoPd{sub 0.80}Co{sub 0.20}, in which disorder is of the quenched random exchange type perturbed by a very weak random anisotropy interaction. The critical exponent {beta} deduced over the range 1 {times} 10{sup {minus}2} < t < 2 {times} 10{sup {minus}1} is 0.385(20), and is consistent with the theoretical prediction for quenched disordered 3d Heisenberg systems: the disorder is irrelevant to the critical behavior. However, because of the restricted range of reduced temperature, the result is insufficiently asymptotic to serve as a conclusive test of the theory. Outside the critical region the distribution of Fe{sup 57} hyperfine field in Pd{sub 0.80}Co{sub 0.20} is observed to have an anomalous temperature dependence characterized by a linear increase in the width of the field distribution for T/T{sub C} {ge} 0.6.« less

Coexistence Curve of Perfluoromethylcyclohexane-Isopropyl Alcohol

NASA Technical Reports Server (NTRS)

Jacobs, D. T.; Kuhl, D. E.; Selby, C. E.

1996-01-01

The coexistence curve of the binary fluid mixture perfluoromethylcyclohexane-isopropyl alcohol was determined by precisely measuring the refractive index both above and below its upper critical consolute point. Sixty-seven two-phase data points were obtained over a wide range of reduced temperatures, 10(exp -5) less than t less than 2.5 x 10(exp -1), to determine the location of the critical point: critical temperature=89.901 C, and critical composition = 62.2% by volume perfluoromethylcyclohexane. These data were analyzed to determine the critical exponent 8 close to the critical point, the amplitude B, and the anomaly in the diameter. The volume-fraction coexistence curve is found to be as symmetric as any composition like variable. Correction to scaling is investigated as well as the need for a crossover theory. A model is proposed that describes the asymptotic approach to zero of the effective exponent Beta, which allows an estimation of the temperature regime free of crossover effects.

Hybrid phase transition into an absorbing state: Percolation and avalanches

NASA Astrophysics Data System (ADS)

Lee, Deokjae; Choi, S.; Stippinger, M.; Kertész, J.; Kahng, B.

2016-04-01

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or "infinite" avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent βm of the order parameter is 1 /2 under general conditions, while the value of the exponent γm characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, βa and γa. These two critical behaviors are coupled by a scaling law: 1 -βm=γa .

Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

NASA Astrophysics Data System (ADS)

Salerno, K. Michael; Robbins, Mark O.

2013-12-01

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with 103-106 particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

Entanglement entropy in the long-range Kitaev chain

NASA Astrophysics Data System (ADS)

Ares, Filiberto; Esteve, José G.; Falceto, Fernando; de Queiroz, Amilcar R.

2018-06-01

In this paper we complete the study on the asymptotic behavior of the entanglement entropy for Kitaev chains with long-range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost. We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a technique for computing the asymptotic behavior of block Toeplitz determinants with discontinuous symbols has been developed.

Critical phases in the raise and peel model

NASA Astrophysics Data System (ADS)

Jara, D. A. C.; Alcaraz, F. C.

2018-05-01

The raise and peel model (RPM) is a nonlocal stochastic model describing the space and time fluctuations of an evolving one dimensional interface. Its relevant parameter u is the ratio between the rates of local adsorption and nonlocal desorption processes (avalanches) The model at u  =  1 is the first example of a conformally invariant stochastic model. For small values u  <  u 0 the model is known to be noncritical, while for u  >  u 0 it is critical. Although previous studies indicate that u 0  =  1, a determination of u 0 with a reasonable precision is still missing. By calculating numerically the structure function of the height profiles in the reciprocal space we confirm with good precision that indeed u 0  =  1. We establish that at the conformal invariant point u  =  1 the RPM has a roughening transition with dynamical and roughness critical exponents z  =  1 and , respectively. For u  >  1 the model is critical with a u-dependent dynamical critical exponent that tends towards zero as . However at 1/u  =  0 the RPM is exactly mapped into the totally asymmetric exclusion problem. This last model is known to be noncritical (critical) for open (periodic) boundary conditions. Our numerical studies indicate that the RPM as , due to its nonlocal dynamical processes, has the same large-distance physics no matter what boundary condition we chose. For u  >  1, our numerical analysis shows that in contrast to previous predictions, the region is composed of two distinct critical phases. For the height profiles are rough (), and for the height profiles are flat at large distances (). We also observed that in both critical phases (u  >  1) the RPM at short length scales, has an effective behavior in the Kardar–Parisi–Zhang critical universality class, that is not the true behavior of the system at large length scales.

Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice

NASA Astrophysics Data System (ADS)

Perino, E. J.; Matoz-Fernandez, D. A.; Pasinetti, P. M.; Ramirez-Pastor, A. J.

2017-07-01

Monte Carlo simulations and finite-size scaling analysis have been performed to study the jamming and percolation behavior of linear k-mers (also known as rods or needles) on a two-dimensional triangular lattice of linear dimension L, considering an isotropic RSA process and periodic boundary conditions. Extensive numerical work has been done to extend previous studies to larger system sizes and longer k-mers, which enables the confirmation of a nonmonotonic size dependence of the percolation threshold and the estimation of a maximum value of k from which percolation would no longer occur. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system is not affected, having the same universality class of the ordinary random percolation.

Unified presentation of four fundamental inequalities

NASA Astrophysics Data System (ADS)

Lajzerowicz, Joseph; Lehoucq, Roland; Graner, François

2018-03-01

We suggest an unified presentation to teach fundamental constants to graduate students, by introducing four lower limits to observed phenomena. The reduced Planck constant ℏ is the lowest classically definable action. The inverse of invariant speed, s, is the lowest observable slowness. The Planck time, {t}{{P}}, is the lowest observable time scale. The Boltzmann constant, k, determines the lowest coherent degree of freedom; we recall an Einstein criterion on the fluctuations of small thermal systems and show that it has far-reaching implications, such as demonstrating the relations between critical exponents. Each of these four fundamental limits enters in an inequality, which marks a horizon of the Universe we can perceive. This compact presentation can resolve some difficulties encountered when trying to defining the epistemologic status of these constants, and emphasizes their useful role in shaping our intuitive vision of the Universe.

Out-of-equilibrium dynamics driven by localized time-dependent perturbations at quantum phase transitions

NASA Astrophysics Data System (ADS)

Pelissetto, Andrea; Rossini, Davide; Vicari, Ettore

2018-03-01

We investigate the quantum dynamics of many-body systems subject to local (i.e., restricted to a limited space region) time-dependent perturbations. If the system crosses a quantum phase transition, an off-equilibrium behavior is observed, even for a very slow driving. We show that, close to the transition, time-dependent quantities obey scaling laws. In first-order transitions, the scaling behavior is universal, and some scaling functions can be computed exactly. For continuous transitions, the scaling laws are controlled by the standard critical exponents and by the renormalization-group dimension of the perturbation at the transition. Our protocol can be implemented in existing relatively small quantum simulators, paving the way for a quantitative probe of the universal off-equilibrium scaling behavior, without the need to manipulate systems close to the thermodynamic limit.

Superconductor-insulator quantum phase transition in disordered FeSe thin films.

PubMed

Schneider, R; Zaitsev, A G; Fuchs, D; V Löhneysen, H

2012-06-22

The evolution of two-dimensional electronic transport with increasing disorder in epitaxial FeSe thin films is studied. Disorder is generated by reducing the film thickness. The extreme sensitivity of the films to disorder results in a superconductor-insulator transition. The finite-size scaling analysis in the critical regime based on the Bose-glass model strongly supports the idea of a continuous quantum phase transition. The obtained value for the critical-exponent product of approximately 7/3 suggests that the transition is governed by quantum percolation. Finite-size scaling with the same critical-exponent product is also substantiated when the superconductor-insulator transition is tuned with an applied magnetic field.

Quantum criticality of the two-channel pseudogap Anderson model: universal scaling in linear and non-linear conductance.

PubMed

Wu, Tsan-Pei; Wang, Xiao-Qun; Guo, Guang-Yu; Anders, Frithjof; Chung, Chung-Hou

2016-05-05

The quantum criticality of the two-lead two-channel pseudogap Anderson impurity model is studied. Based on the non-crossing approximation (NCA) and numerical renormalization group (NRG) approaches, we calculate both the linear and nonlinear conductance of the model at finite temperatures with a voltage bias and a power-law vanishing conduction electron density of states, ρc(ω) proportional |ω − μF|(r) (0 < r < 1) near the Fermi energy μF. At a fixed lead-impurity hybridization, a quantum phase transition from the two-channel Kondo (2CK) to the local moment (LM) phase is observed with increasing r from r = 0 to r = rc < 1. Surprisingly, in the 2CK phase, different power-law scalings from the well-known [Formula: see text] or [Formula: see text] form is found. Moreover, novel power-law scalings in conductances at the 2CK-LM quantum critical point are identified. Clear distinctions are found on the critical exponents between linear and non-linear conductance at criticality. The implications of these two distinct quantum critical properties for the non-equilibrium quantum criticality in general are discussed.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

NASA Astrophysics Data System (ADS)

Pan, Xue; Zhang, Yanhua; Chen, Lizhu; Xu, Mingmei; Wu, Yuanfang

2018-01-01

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class. Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

NASA Astrophysics Data System (ADS)

Granato, Enzo

2017-11-01

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or π junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.

Quantum Griffiths singularity of superconductor-metal transition in Ga thin films.

PubMed

Xing, Ying; Zhang, Hui-Min; Fu, Hai-Long; Liu, Haiwen; Sun, Yi; Peng, Jun-Ping; Wang, Fa; Lin, Xi; Ma, Xu-Cun; Xue, Qi-Kun; Wang, Jian; Xie, X C

2015-10-30

The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions. Copyright © 2015, American Association for the Advancement of Science.

Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

NASA Astrophysics Data System (ADS)

Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa

2016-11-01

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.

Second Sound Measurements Very Near the Lambda Point

NASA Technical Reports Server (NTRS)

Adriaans, M.; Lipa, J.

1999-01-01

The sound was generated by wire-wound heaters embedded in the end opposite the sensor in each cavity. The superfluid density was determined from second sound measurements and the critical exponent v was obtained from fits to the data. The results from the exponent were found to be very sensitive to the treatment of systematic effects in the data.

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

NASA Astrophysics Data System (ADS)

Pompe, B.; Leven, R. W.

1988-11-01

We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.

Tests of nonuniversality of the stock return distributions in an emerging market

NASA Astrophysics Data System (ADS)

Mu, Guo-Hua; Zhou, Wei-Xing

2010-12-01

There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that the tail exponents are universal at least for mature markets in the sense that they do not depend on stock market, industry sector, and market capitalization. We investigate the distributions of intraday returns at different time scales ( Δt=1 , 5, 15, and 30 min) of all the A-share stocks traded in the Chinese stock market, which is the largest emerging market in the world. We find that the returns can be well fitted by the q -Gaussian distribution and the tails have power-law relaxations with the exponents increasing with Δt and being well outside the Lévy stable regime for individual stocks. We provide statistically significant evidence showing that, at small time scales Δt<15min , the exponents logarithmically decrease with the turnover rate and increase with the market capitalization. When Δt>15min , no conclusive evidence is found for a possible dependence of the tail exponent on the turnover rate or the market capitalization. Our findings indicate that the intraday return distributions at small time scales are not universal in emerging stock markets but might be universal at large time scales.

5-D Choptuik critical exponent and holography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bland, J.; Kunstatter, G.

2007-05-15

Recently, a holographic argument was used to relate the saturation exponent, {gamma}{sub BFKL}, of 4-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, {gamma}{sub 5d}, in 5-dimensional black hole formation via scalar field collapse [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.]. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of {gamma}{sub 5d} with substantially decreased numerical error. Our current result is {gamma}{sub 5d}=0.4131{+-}0.0001, which is close to, but not in strict agreement with, the value of {gamma}{sub BFKL}=0.409more » 552 quoted in [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.].« less

Observing golden-mean universality class in the scaling of thermal transport.

PubMed

Xiong, Daxing

2018-02-01

We address the issue of whether the golden-mean [ψ=(sqrt[5]+1)/2≃1.618] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ=5/3, as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.

Observing golden-mean universality class in the scaling of thermal transport

NASA Astrophysics Data System (ADS)

Xiong, Daxing

2018-02-01

We address the issue of whether the golden-mean [ψ =(√{5 }+1 ) /2 ≃1.618 ] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ =5 /3 , as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.

Defect production in nonlinear quench across a quantum critical point.

PubMed

Sen, Diptiman; Sengupta, K; Mondal, Shreyoshi

2008-07-04

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.

Dielectric spectroscopy of polymer-metal composites across the percolation threshold

NASA Astrophysics Data System (ADS)

Panda, Maheswar; Srinivas, V.; Thakur, A. K.

2014-11-01

Polymer (polar/nonpolar)/metal composites (PMC) were prepared under different process conditions. In polar PMC, dipolar relaxation plays a predominant role below percolation threshold (fc) and anomalous low frequency dispersion (ALFD) becomes dominant above fc while ALFD is the only likely possibility for nonpolar PMC above fc. The magnitude of relaxation exponents "m", "p" and "n", evaluated from the experimental results using Jonscher's universal dielectric response (JUDR) laws, falls within the universal limit [0, 1] with additional feature of strong dependence on volume fraction of conductor (fcon). The decrease in the relaxation exponent "m" with an increase of fcon is directly linked with decrease in the number of dipoles of the polymer in the composite and is accompanied by a distribution of relaxation time due to increased heterogeneity of the system. The magnitude of the relaxation exponent "n" decreases at fc, due to the prevalence of Maxwell-Wagner-Sillar polarization contributed by uncorrelated electrons.

Universal rescaling of flow curves for yield-stress fluids close to jamming

NASA Astrophysics Data System (ADS)

Dinkgreve, M.; Paredes, J.; Michels, M. A. J.; Bonn, D.

2015-07-01

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

Light-induced metal-insulator transition in a switchable mirror.

PubMed

Hoekstra, A F; Roy, A S; Rosenbaum, T F; Griessen, R; Wijngaarden, R J; Koeman, N J

2001-06-04

Rare earth hydride films can be converted reversibly from metallic mirrors to insulating windows simply by changing the surrounding hydrogen gas pressure at room temperature. At low temperatures, in situ doping is not possible in this way as hydrogen cannot diffuse. However, our finding of persistent photoconductivity under ultraviolet illumination offers an attractive possibility to tune yttrium hydride through the T = 0 metal-insulator transition. Conductivity and Hall measurements are used to determine critical exponents. The unusually large value for the product of the static and dynamical critical exponents appears to signify the important role played by electron-electron interactions.

Holographic Lifshitz superconductors: Analytic solution

NASA Astrophysics Data System (ADS)

Natsuume, Makoto; Okamura, Takashi

2018-03-01

We construct an analytic solution for a one-parameter family of holographic superconductors in asymptotically Lifshitz spacetimes. We utilize this solution to explore various properties of the systems such as (1) the superfluid phase background and the grand canonical potential, (2) the order parameter response function or the susceptibility, (3) the London equation, and (4) the background with a superfluid flow or a magnetic field. From these results, we identify the dual Ginzburg-Landau theory including numerical coefficients. Also, the dynamic critical exponent zD associated with the critical point is given by zD=2 irrespective of the value of the Lifshitz exponent z .

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory

NASA Astrophysics Data System (ADS)

Yabunaka, Shunsuke; Onuki, Akira

2017-09-01

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980), 10.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ (r ) , where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ (r ) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h1, where the surface order parameter ψ (a ) is determined by h1 and is independent of the radius a . If r considerably exceeds a , ψ (r ) decays as r-(1 +η ) for a sphere and r-(1 +η )/2 for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

NASA Astrophysics Data System (ADS)

Hnatič, M.; Kalagov, G.; Nalimov, M.

2018-01-01

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi 〉 ∼ (Pji⊥ + αPji∥) /k d + ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d = 3, ζ = 4 / 3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α ≲ 2.26. Otherwise, in the case of "strong compressibility" α ≳ 2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Quenched bond randomness: Superfluidity in porous media and the strong violation of universality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Falicov, A.; Berker, A.N.

1997-04-01

The effects of quenched bond randomness are most readily studied with superfluidity immersed in a porous medium. A lattice model for {sup 3}He-{sup 4}He mixtures and incomplete {sup 4}He fillings in aerogel yields the signature effect of bond randomness, namely the conversion of symmetry-breaking first-order phase transitions into second-order phase transitions, the A-line reaching zero temperature, and the elimination of non-symmetry-breaking first-order phase transitions. The model recognizes the importance of the connected nature of aerogel randomness and thereby yields superfluidity at very low {sup 4}He concentrations, a phase separation entirely within the superfluid phase, and the order-parameter contrast between mixturesmore » and incomplete fillings, all in agreement with experiments. The special properties of the helium mixture/aerogel system are distinctly linked to the aerogel properties of connectivity, randomness, and tenuousness, via the additional study of a regularized {open_quote}jungle-gym{close_quotes} aerogel. Renormalization-group calculations indicate that a strong violation of the empirical universality principle of critical phenomena occurs under quenched bond randomness. It is argued that helium/aerogel critical properties reflect this violation and further experiments are suggested. Renormalization-group analysis also shows that, adjoiningly to the strong universality violation (which hinges on the occurrence or non-occurrence of asymptotic strong coupling-strong randomness under resealing), there is a new {open_quotes}hyperuniversality{close_quotes} at phase transitions with asymptotic strong coupling-strong randomness behavior, for example assigning the same critical exponents to random-bond tricriticality and random-field criticality.« less

Rotationally symmetric viscous gas flows

NASA Astrophysics Data System (ADS)

Weigant, W.; Plotnikov, P. I.

2017-03-01

The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.

Dynamics of social contagions with limited contact capacity.

PubMed

Wang, Wei; Shu, Panpan; Zhu, Yu-Xiao; Tang, Ming; Zhang, Yi-Cheng

2015-10-01

Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacities. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each adopted individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. There is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.

Coherent-Anomaly Method in Critical Phenomena. IV. Study of the Wave-Number-Dependent Susceptibility in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

1988-03-01

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν{\\cdot}ηi{=}β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Slow Relaxation in Anderson Critical Systems

NASA Astrophysics Data System (ADS)

Choi, Soonwon; Yao, Norman; Choi, Joonhee; Kucsko, Georg; Lukin, Mikhail

2016-05-01

We study the single particle dynamics in disordered systems with long range hopping, focusing on the critical cases, i.e., the hopping amplitude decays as 1 /rd in d-dimension. We show that with strong on-site potential disorder, the return probability of the particle decays as power-law in time. As on-site potential disorder decreases, the temporal profile smoothly changes from a simple power-law to the sum of multiple power-laws with exponents ranged from 0 to νmax. We analytically compute the decay exponents using a simple resonance counting argument, which quantitatively agrees with exact numerical results. Our result implies that the dynamics in Anderson Critical systems are dominated by resonances. Harvard-MIT CUA, Kwanjeong Educational Fellowship, AFOSR MURI, Samsung Scholarship.

Quantum influence in the criticality of the spin- {1}/{2} anisotropic Heisenberg model

NASA Astrophysics Data System (ADS)

Ricardo de Sousa, J.; Araújo, Ijanílio G.

1999-07-01

We study the spin- {1}/{2} anisotropic Heisenberg antiferromagnetic model using the effective field renormalization group (EFRG) approach. The EFRG method is illustrated by employing approximations in which clusters with one ( N'=1) and two ( N=2) spins are used. The dependence of the critical temperature Tc (ferromagnetic-F case) and TN (antiferromagnetic-AF case) and thermal critical exponent, Yt, are obtained as a function of anisotropy parameter ( Δ) on a simple cubic lattice. We find that, in our results, TN is higher than Tc for the quantum anisotropic Heisenberg limit and TN= Tc for the Ising and quantum XY limits. We have also shown that the thermal critical exponent Yt for the isotropic Heisenberg model shows a small dependence on the type of interaction (F or AF) due to finite size effects.

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

Lyapunov exponents of stochastic systems—from micro to macro

NASA Astrophysics Data System (ADS)

Laffargue, Tanguy; Tailleur, Julien; van Wijland, Frédéric

2016-03-01

Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the ‘same noise realization’. The purpose of this work is to critically examine what this expression means. For Brownian particles, we consider two natural interpretations of the noise: intrinsic to the particles or stemming from the fluctuations of the environment. We show how they lead to different distributions of the largest Lyapunov exponent as well as different fluctuating hydrodynamics for the collective density field. We discuss, both at microscopic and macroscopic levels, the limits in which these noise prescriptions become equivalent. We close this paper by providing an estimate of the largest Lyapunov exponent and of its fluctuations for interacting particles evolving with Dean-Kawasaki dynamics.

Flux line relaxation kinetics following current quenches in disordered type-II superconductors

NASA Astrophysics Data System (ADS)

Chaturvedi, Harshwardhan; Assi, Hiba; Dobramysl, Ulrich; Pleimling, Michel; Täuber, Uwe

We describe the disordered vortex system in type-II superconductors with an elastic line model, whose dynamics we investigate numerically by means of Langevin Molecular Dynamics. A system of driven interacting flux lines in a sample with randomly distributed point pinning centers is subjected to drive quench from a moving non-equilibrium steady state into one of three regimes viz. moving (steady state), pinned (glassy) or depinning (critical). The first yields fast exponential relaxation to the new non-equilibrium stationary state while the second displays algebraically slow relaxation and aging scaling with non-universal exponents. Our most recent work consists of aging and finite temperature scaling studies for drive quenches into the critical depinning regime. This research is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.

Critical behavior of the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.; Fehske, Holger

2018-05-01

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V / U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c = 1 / 2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c = 7 / 10 . We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β = 1 / 8 (1/24) and correlation length ν = 1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

Symmetry breaking by heating in a continuous opinion model

NASA Astrophysics Data System (ADS)

Anteneodo, Celia; Crokidakis, Nuno

2017-04-01

We study the critical behavior of a continuous opinion model, driven by kinetic exchanges in a fully connected population. Opinions range in the real interval [-1 ,1 ] , representing the different shades of opinions against and for an issue under debate. Individuals' opinions evolve through pairwise interactions, with couplings that are typically positive, but a fraction p of negative ones is allowed. Moreover, a social temperature parameter T controls the tendency of the individual responses toward neutrality. Depending on p and T , different collective states emerge: symmetry broken (one side wins), symmetric (tie of opposite sides), and absorbing neutral (indecision wins). We find the critical points and exponents that characterize the phase transitions between them. The symmetry breaking transition belongs to the usual Ising mean-field universality class, but the absorbing-phase transitions, with β =0.5 , are out of the paradigmatic directed percolation class. Moreover, ordered phases can emerge by increasing social temperature.

Potts-model formulation of the random resistor network

NASA Astrophysics Data System (ADS)

Harris, A. B.; Lubensky, T. C.

1987-05-01

The randomly diluted resistor network is formulated in terms of an n-replicated s-state Potts model with a spin-spin coupling constant J in the limit when first n, then s, and finally 1/J go to zero. This limit is discussed and to leading order in 1/J the generalized susceptibility is shown to reproduce the results of the accompanying paper where the resistor network is treated using the xy model. This Potts Hamiltonian is converted into a field theory by the usual Hubbard-Stratonovich transformation and thereby a renormalization-group treatment is developed to obtain the corrections to the critical exponents to first order in ɛ=6-d, where d is the spatial dimensionality. The recursion relations are shown to be the same as for the xy model. Their detailed analysis (given in the accompanying paper) gives the resistance crossover exponent as φ1=1+ɛ/42, and determines the critical exponent, t for the conductivity of the randomly diluted resistor network at concentrations, p, just above the percolation threshold: t=(d-2)ν+φ1, where ν is the critical exponent for the correlation length at the percolation threshold. These results correct previously accepted results giving φ=1 to all orders in ɛ. The new result for φ1 removes the paradox associated with the numerical result that t>1 for d=2, and also shows that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, since it disagrees with the ɛ expansion.

Spectral dimension of the universe in quantum gravity at a lifshitz point.

PubMed

Horava, Petr

2009-04-24

We extend the definition of "spectral dimension" d_{s} (usually defined for fractal and lattice geometries) to theories in spacetimes with anisotropic scaling. We show that in gravity with dynamical critical exponent z in D+1 dimensions, the spectral dimension of spacetime is d_{s}=1+D/z. In the case of gravity in 3+1 dimensions with z=3 in the UV which flows to z=1 in the IR, the spectral dimension changes from d_{s}=4 at large scales to d_{s}=2 at short distances. Remarkably, this is the behavior found numerically by Ambjørn et al. in their causal dynamical triangulations approach to quantum gravity.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Passot, T.; Sulem, P. L., E-mail: passot@oca.eu, E-mail: sulem@oca.eu

A phenomenological turbulence model for kinetic Alfvén waves in a magnetized collisionless plasma that is able to reproduce the non-universal power-law spectra observed at the sub-ion scales in the solar wind and the terrestrial magnetosphere is presented. The process of temperature homogenization along distorted magnetic field lines, induced by Landau damping, affects the turbulence transfer time and results in a steepening of the sub-ion power-law spectrum of critically balanced turbulence, whose exponent is sensitive to the ratio between the Alfvén wave period and the nonlinear timescale. Transition from large-scale weak turbulence to smaller scale strong turbulence is captured and nonlocalmore » interactions, relevant in the case of steep spectra, are accounted for.« less

Influence of Ti Doping on the Critical Behavior and Magnetocaloric Effect in Disordered Ferromagnets La0.7Ba0.3Mn1- x Ti x O3

NASA Astrophysics Data System (ADS)

Ho, T. A.; Phan, M. H.; Phuc, N. X.; Lam, V. D.; Phan, T. L.; Yu, S. C.

2016-05-01

The Ti-substitution influence on the magnetic and magnetocaloric properties of La0.7Ba0.3Mn1- x Ti x O3 ( x = 0.05 and 0.1) was investigated. Based on Banerjee's criteria and Franco's universal curves, we proved the existence of a second-order magnetic phase transition in the samples. Using the modified Arrott plot method, we determined the critical parameters T C ≈ 245 K, β = 0.374 ± 0.013, γ = 1.228 ± 0.045, and δ = 4.26 ± 0.03 for x = 0.05, and T C ≈ 169 K, β = 0.339 ± 0.001, γ = 1.307 ± 0.003, and δ = 4.78 ± 0.02 for x = 0.1. With these critical values, the predictable scaling behavior of the M( H) data above and below T C proves that the calculated exponents are unambiguous and intrinsic. The values β = 0.374 for x = 0.05 and β = 0.339 for x = 0.1 suggest that the magnetic phase transition of the samples falls into the three-dimensional (3D) Heisenberg and 3D Ising universality classes, respectively, corresponding to short-range ferromagnetic (FM) order due to FM clusters in a wide temperature range even above T C, as confirmed by electron spin resonance studies. In reference to the magnetocaloric effect around T C, the magnetic entropy change reaches maximum values (|ΔSmax|) of about 4 and 3 J kg-1 K-1 for x = 0.05 and 0.1, respectively, for a magnetic field change 50 kOe. Magnetic field dependencies of |ΔSmax| obey a power function |ΔSmax( H)| ∝ H n , where exponent values n = 0.59 and 0.61 for x = 0.05 and 0.1, respectively, were determined from the relation n = 1 + ( β-1)/( β + γ). The difference between the experimental n values and the theoretical value n = 2/3 of the mean field model is due to the presence of short-range FM order in the samples.

The critical crossover at the n-hexane-water interface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tikhonov, A. M., E-mail: tikhonov@kapitza.ras.r

According to estimates of the parameters of the critical crossover in monolayers of long-chain alcohol molecules adsorbed at the n-hexane-water interface, all systems in which this phenomenon is observed are characterized by the same value of the critical exponent {nu} {approx} 1.8.

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory.

PubMed

Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat

2016-06-01

The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Genetic Algorithms and Nucleation in VIH-AIDS transition.

NASA Astrophysics Data System (ADS)

Barranon, Armando

2003-03-01

VIH to AIDS transition has been modeled via a genetic algorithm that uses boom-boom principle and where population evolution is simulated with a cellular automaton based on SIR model. VIH to AIDS transition is signed by nucleation of infected cells and low probability of infection are obtained for different mutation rates in agreement with clinical results. A power law is obtained with a critical exponent close to the critical exponent of cubic, spherical percolation, colossal magnetic resonance, Ising Model and liquid-gas phase transition in heavy ion collisions. Computations were carried out at UAM-A Supercomputing Lab and author acknowledges financial support from Division of CBI at UAM-A.

Impact of network topology on self-organized criticality

NASA Astrophysics Data System (ADS)

Hoffmann, Heiko

2018-02-01

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites. Then, we hypothesize that SOC relies on the formation process of these clusters, and present a model of such formation. For low-dimensional networks, we show theoretically and in simulation that the exponent of the cluster-size distribution is proportional to the ratio of the fractal dimension of the cluster boundary and the dimensionality of the network. For the BTW model, in our simulations, the exponent of the avalanche-area distribution matched approximately our prediction based on this ratio for two-dimensional networks, but deviated for higher dimensions. We hypothesize a transition from cluster formation to the mean-field theory process with increasing dimensionality. This work sheds light onto the mechanisms behind SOC, particularly, the impact of the network topology.

Probing the critical exponent of the superfluid fraction in a strongly interacting Fermi gas

NASA Astrophysics Data System (ADS)

Hu, Hui; Liu, Xia-Ji

2013-11-01

We theoretically investigate the critical behavior of a second-sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature Tc, the frequency or the sound velocity of the second-sound mode crucially depends on the critical exponent β of the superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like (1-T/Tc)β-1/2 when β<1/2. In a highly elongated trap, the speed of the second sound reduces by a factor of 1/2β+1 from that in a homogeneous three-dimensional superfluid. Our prediction could readily be tested by measurements of second-sound wave propagation in a setup, such as that exploited by Sidorenkov [Nature (London)NATUAS0028-083610.1038/nature12136 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.

FAST TRACK COMMUNICATION Critical exponents of domain walls in the two-dimensional Potts model

NASA Astrophysics Data System (ADS)

Dubail, Jérôme; Lykke Jacobsen, Jesper; Saleur, Hubert

2010-12-01

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e. connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{\\ell _1-\\ell _2,2\\ell _1}, valid for 0 <= Q <= 4, that describe the insertion of ell1 thin and ell2 thick domain walls.

Role of initial correlation in coarsening of a ferromagnet

NASA Astrophysics Data System (ADS)

Chakraborty, Saikat; Das, Subir K.

2015-06-01

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions d = 2 and 3, on square and simple cubic lattices. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures (Tf) below the critical one (Tc), from different initial temperatures Ti ≥ Tc. In long time limit, for Ti>Tc, the persistence probability exhibits power-law decay with exponents θ ≃ 0.22 and ≃ 0.18 in d = 2 and 3, respectively. For finite Ti, the early time behavior is a different power-law whose life-time diverges and exponent decreases as Ti → Tc. The two steps are connected via power-law as a function of domain length and the crossover to the second step occurs when this characteristic length exceeds the equilibrium correlation length at T = Ti. Ti = Tc is expected to provide a new universality class for which we obtain θ ≡ θc ≃ 0.035 in d = 2 and ≃0.105 in d = 3. The time dependence of the average domain size ℓ, however, is observed to be rather insensitive to the choice of Ti.

Origin of Noncubic Scaling Law in Disordered Granular Packing.

PubMed

Xia, Chengjie; Li, Jindong; Kou, Binquan; Cao, Yixin; Li, Zhifeng; Xiao, Xianghui; Fu, Yanan; Xiao, Tiqiao; Hong, Liang; Zhang, Jie; Kob, Walter; Wang, Yujie

2017-06-09

Recent diffraction experiments on metallic glasses have unveiled an unexpected noncubic scaling law between density and average interatomic distance, which led to the speculation of the presence of fractal glass order. Using x-ray tomography we identify here a similar noncubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within the first nearest neighbor shell, and, therefore, is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with a contact number around 6, and we argue that the exponent should not be universal.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

PubMed

Leibovich, N; Dechant, A; Lutz, E; Barkai, E

2016-11-01

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

Scaling in nature: From DNA through heartbeats to weather

NASA Astrophysics Data System (ADS)

Havlin, S.; Buldyrev, S. V.; Bunde, A.; Goldberger, A. L.; Ivanov, P. Ch.; Peng, C.-K.; Stanley, H. E.

1999-12-01

The purpose of this talk is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent α quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent α is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

Scaling in nature: from DNA through heartbeats to weather

NASA Technical Reports Server (NTRS)

Havlin, S.; Buldyrev, S. V.; Bunde, A.; Goldberger, A. L.; Peng, C. K.; Stanley, H. E.

1999-01-01

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.

A Brief Survey of the Equilibrium and Transport Properties of Critical Fluids and the Degree to Which Microgravity is Required for Their Experimental Investigation

NASA Technical Reports Server (NTRS)

Ferrell, Richard A.

1996-01-01

The modern theory of second order phase transitions is very successful in calculating the critical exponents as an asymptotic expansion in powers of epsilon = 4 - D, the deviation of D = 3, the spatial dimension of the actual physical system from that of the abstract four-dimensional reference model. This remarkable mathematical 'tour de force' leaves unanswered, however, many fundamental questions concerning the exact nature of how the fluctuations interact. I discuss here some experiments which would help to further our understanding of the equilibrium critical properties. Especially promising would be a measurement of the temperature dependence of the turbidity very close to the critical point. This has the promise of determining the small and elusive but fundamentally important anomalous dimension exponent eta. I also review various ways of measuring the critical transport coefficients and point out some cases where ground based experiments may usefully supplement flight experiments.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Relative permeability of hydrate-bearing sediments from percolation theory and critical path analysis: theoretical and experimental results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daigle, Hugh; Rice, Mary Anna; Daigle, Hugh

Relative permeabilities to water and gas are important parameters for accurate modeling of the formation of methane hydrate deposits and production of methane from hydrate reservoirs. Experimental measurements of gas and water permeability in the presence of hydrate are difficult to obtain. The few datasets that do exist suggest that relative permeability obeys a power law relationship with water or gas saturation with exponents ranging from around 2 to greater than 10. Critical path analysis and percolation theory provide a framework for interpreting the saturation-dependence of relative permeability based on percolation thresholds and the breadth of pore size distributions, whichmore » may be determined easily from 3-D images or gas adsorption-desorption hysteresis. We show that the exponent of the permeability-saturation relationship for relative permeability to water is related to the breadth of the pore size distribution, with broader pore size distributions corresponding to larger exponents. Relative permeability to water in well-sorted sediments with narrow pore size distributions, such as Berea sandstone or Toyoura sand, follows percolation scaling with an exponent of 2. On the other hand, pore-size distributions determined from argon adsorption measurements we performed on clays from the Nankai Trough suggest that relative permeability to water in fine-grained intervals may be characterized by exponents as large as 10 as determined from critical path analysis. We also show that relative permeability to the gas phase follows percolation scaling with a quadratic dependence on gas saturation, but the threshold gas saturation for percolation changes with hydrate saturation, which is an important consideration in systems in which both hydrate and gas are present, such as during production from a hydrate reservoir. Our work shows how measurements of pore size distributions from 3-D imaging or gas adsorption may be used to determine relative permeabilities.« less

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

NASA Astrophysics Data System (ADS)

Sharma, A.; Licup, A. J.; Rens, R.; Vahabi, M.; Jansen, K. A.; Koenderink, G. H.; MacKintosh, F. C.

2016-10-01

Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016), 10.1038/nphys3628]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.

Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition

NASA Astrophysics Data System (ADS)

Kudo, Kazue; Deguchi, Tetsuo

2018-06-01

We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 X X Z spin chain with a random field by studying level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the ratio of adjacent level spacings, and thus, extend previous studies in which interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d-dimensional regular lattices.

PubMed

Dias, W S; Bertrand, D; Lyra, M L

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d -dimensional regular lattices

NASA Astrophysics Data System (ADS)

Dias, W. S.; Bertrand, D.; Lyra, M. L.

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .

Estimation of critical behavior from the density of states in classical statistical models

NASA Astrophysics Data System (ADS)

Malakis, A.; Peratzakis, A.; Fytas, N. G.

2004-12-01

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

Domain-area distribution anomaly in segregating multicomponent superfluids

NASA Astrophysics Data System (ADS)

Takeuchi, Hiromitsu

2018-01-01

The domain-area distribution in the phase transition dynamics of Z2 symmetry breaking is studied theoretically and numerically for segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Due to the dynamic-scaling law of the phase ordering kinetics, the domain-area distribution is described by a universal function of the domain area, rescaled by the mean distance between domain walls. The scaling theory for general coarsening dynamics in two dimensions hypothesizes that the distribution during the coarsening dynamics has a hierarchy with the two scaling regimes, the microscopic and macroscopic regimes with distinct power-law exponents. The power law in the macroscopic regime, where the domain size is larger than the mean distance, is universally represented with the Fisher's exponent of the percolation theory in two dimensions. On the other hand, the power-law exponent in the microscopic regime is sensitive to the microscopic dynamics of the system. This conjecture is confirmed by large-scale numerical simulations of the coupled Gross-Pitaevskii equation for binary condensates. In the numerical experiments of the superfluid system, the exponent in the microscopic regime anomalously reaches to its theoretical upper limit of the general scaling theory. The anomaly comes from the quantum-fluid effect in the presence of circular vortex sheets, described by the hydrodynamic approximation neglecting the fluid compressibility. It is also found that the distribution of superfluid circulation along vortex sheets obeys a dynamic-scaling law with different power-law exponents in the two regimes. An analogy to quantum turbulence on the hierarchy of vorticity distribution and the applicability to chiral superfluid 3He in a slab are also discussed.

Random Walks on Cartesian Products of Certain Nonamenable Groups and Integer Lattices

NASA Astrophysics Data System (ADS)

Vishnepolsky, Rachel

A random walk on a discrete group satisfies a local limit theorem with power law exponent \\alpha if the return probabilities follow the asymptotic law. P{ return to starting point after n steps } ˜ Crhonn-alpha.. A group has a universal local limit theorem if all random walks on the group with finitely supported step distributions obey a local limit theorem with the same power law exponent. Given two groups that obey universal local limit theorems, it is not known whether their cartesian product also has a universal local limit theorem. We settle the question affirmatively in one case, by considering a random walk on the cartesian product of a nonamenable group whose Cayley graph is a tree, and the integer lattice. As corollaries, we derive large deviations estimates and a central limit theorem.

Fermion bag approach to Hamiltonian lattice field theories in continuous time

NASA Astrophysics Data System (ADS)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.

Origin of Noncubic Scaling Law in Disordered Granular Packing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Chengjie; Li, Jindong; Kou, Binquan

Recent diffraction experiments on metallic glasses have unveiled an unexpected non-cubic scaling law between density and average interatomic distance, which lead to the speculations on the presence of fractal glass order. Using X-ray tomography we identify here a similar non-cubic scaling law in disordered granular packing of spherical particles. We find that the scaling law is directly related to the contact neighbors within first nearest neighbor shell, and therefore is closely connected to the phenomenon of jamming. The seemingly universal scaling exponent around 2.5 arises due to the isostatic condition with contact number around 6, and we argue that themore » exponent should not be universal.« less

Replica approach to mean-variance portfolio optimization

NASA Astrophysics Data System (ADS)

Varga-Haszonits, Istvan; Caccioli, Fabio; Kondor, Imre

2016-12-01

We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the solution does not need to be assumed, but emerges as the unique solution of the optimization problem. We also check the stability of this solution and find that the eigenvalues of the Hessian are positive for r  =  N/T  <  1, where N is the dimension of the portfolio and T the length of the time series used to estimate the covariance matrix. At the critical point r  =  1 a phase transition is taking place. The out of sample estimation error blows up at this point as 1/(1  -  r), independently of the covariance matrix or the expected return, displaying the universality not only of the critical exponent, but also the critical point. As a conspicuous illustration of the dangers of in-sample estimates, the optimal in-sample variance is found to vanish at the critical point inversely proportional to the divergent estimation error.

Singular Valence Fluctuations at a Kondo Destroyed Quantum Critical Point

NASA Astrophysics Data System (ADS)

Pixley, Jedediah; Kirchner, Stefan; Ingersent, Kevin; Si, Qimiao

2012-02-01

Recent experiments on the heavy fermion superconductor beta-YbAlB4 have indicated that this compound satisfies quantum critical scaling [1]. Motivated by the observation of mixed valency in this material [2], we study the Kondo destruction physics in the mixed-valence regime [3] of a particle-hole asymmetric Anderson impurity model with a pseudogapped density of states. In the vicinity of the quantum critical point we determine the finite temperature spin and charge susceptibilities by utilizing a continuous time quantum Monte Carlo method [4] and the numerical renormalization group. We show that this mixed-valence quantum critical point displays a Kondo breakdown effect. Furthermore, we find that both dynamic spin and charge susceptibilities obey frequency over temperature scaling, and that the static charge susceptibility diverges with a universal exponent. Possible implications of our results for beta-YbAlB4 are discussed. [1] Matsumoto et al, Science 331, 316 (2011). [2] Okawaet al, Physical Review Letters 104, 247201 (2010). [3] J. H. Pixley, S. Kirchner, Kevin Ingersent and Q. Si, arXiv:1108.5227v1 (2011). [4] M. Glossop, S. Kirchner, J. H. Pixley and Q. Si, Phys. Rev. Lett. 107, 076404 (2011).

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Thermodynamic scaling of dynamics in polymer melts: predictions from the generalized entropy theory.

PubMed

Xu, Wen-Sheng; Freed, Karl F

2013-06-21

Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ(γ)∕T, where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ~50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.

Global entanglement and quantum phase transitions in the transverse XY Heisenberg chain

NASA Astrophysics Data System (ADS)

Radgohar, Roya; Montakhab, Afshin

2018-01-01

We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach (MW) measure of (global) entanglement. Such a measure, while being readily evaluated, is a multipartite measure of entanglement as opposed to more commonly used bipartite measures. Consequently, we obtain analytic expression of the measure for finite-size systems and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the isotropic (XX) model and show that global entanglement can precisely identify the level-crossing points. The critical exponent for the isotropic transition is obtained exactly from an analytic expression for global entanglement in the thermodynamic limit. Next, the general behavior of the measure is calculated in the thermodynamic limit considering the important role of symmetries for this limit. The so-called oscillatory transition in the ferromagnetic regime can only be characterized by the thermodynamic limit where global entanglement is shown to be zero on the transition curve. Finally, the anisotropic transition is explored where it is shown that global entanglement exhibits an interesting behavior in the finite-size limit. In the thermodynamic limit, we show that global entanglement shows a cusp singularity across the Ising and anisotropic transition, while showing non-analytic behavior at the XX multicritical point. It is concluded that global entanglement, despite its relative simplicity, can be used to identify all the rich structure of the ground-state Heisenberg chain.

Effect of nanowire curviness on the percolation resistivity of transparent, conductive metal nanowire networks

NASA Astrophysics Data System (ADS)

Hicks, Jeremy; Li, Junying; Ying, Chen; Ural, Ant

2018-05-01

We study the effect of nanowire curviness on the percolation resistivity of transparent, conductive metal nanowire networks by Monte Carlo simulations. We generate curvy nanowires as one-dimensional sticks using 3rd-order Bézier curves. The degree of curviness in the network is quantified by the concept of curviness angle and curl ratio. We systematically study the interaction between the effect of curviness and five other nanowire/device parameters on the network resistivity, namely nanowire density, nanowire length, device length, device width, and nanowire alignment. We find that the resistivity exhibits a power law dependence on the curl ratio, which is a signature of percolation transport. In each case, we extract the power-law scaling critical exponents and explain the results using geometrical and physical arguments. The value of the curl ratio critical exponent is not universal, but increases as the other nanowire/device parameters drive the network toward the percolation threshold. We find that, for randomly oriented networks, curviness is undesirable since it increases the resistivity. For well-aligned networks, on the other hand, some curviness is highly desirable, since the resistivity minimum occurs for partially curvy nanowires. We explain these results by considering the two competing effects of curviness on the percolation resistivity. The results presented in this work can be extended to any network, film, or nanocomposite consisting of one-dimensional nanoelements. Our results show that Monte Carlo simulations are an essential predictive tool for both studying the percolation transport and optimizing the electronic properties of transparent, conductive nanowire networks for a wide range of applications.

Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ɛ-Expansion

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts.; Vorob'eva, S. E.; Ivanova, E. V.; Kompaniets, M. V.

2018-04-01

Using the representation for renormalization group functions in terms of nonsingular integrals, we calculate the dynamical critical exponents in the model of critical dynamics of ferromagnets in the fourth order of the ɛ-expansion. We calculate the Feynman diagrams using the sector decomposition technique generalized to critical dynamics problems.

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

NASA Astrophysics Data System (ADS)

Tamarit, F. A.; Cannas, S. A.; Tsallis, C.

1998-03-01

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z.

Determination of the magnetization scaling exponent for single-crystal La0.8Sr0.2MnO3 by broadband microwave surface impedance measurements

NASA Astrophysics Data System (ADS)

Schwartz, Andrew; Scheffler, Marc; Anlage, Steven M.

2000-01-01

Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, ZS(ω,T), of single-crystal La0.8Sr0.2MnO3, as a function of frequency (0.045-45 GHz) and temperature (250-325 K). Through the dependence of the microwave surface impedance on the magnetic permeability, μ⁁(ω,T), we have studied the local magnetic behavior of this material, and have extracted the spontaneous magnetization, M0(T), in zero applied field. The broadband nature of these measurements and the fact that no external field is applied to the material provide a unique opportunity to analyze the critical behavior of the spontaneous magnetization at temperatures very close to the ferromagnetic phase transition. We find a Curie temperature TC=305.5+/-0.5 K and scaling exponent β=0.45+/-0.05, in agreement with the prediction of mean-field theory. We also discuss other recent determinations of the magnetization critical exponent in this and similar materials and show why our results are more definitive.

Scaling laws for impact fragmentation of spherical solids.

PubMed

Timár, G; Kun, F; Carmona, H A; Herrmann, H J

2012-07-01

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

Cost Benefit Assessment of Candidate Decision Aids for Naval Air ASW.

DTIC Science & Technology

1981-09-01

and I respectively), the value of the term where they appear has an increasingly pronounced effect. The exponents were included simply to limit the...effect of these terms to the cases when the limits are very nearly reached. The difference in exponents reflects giving more weight to T than to S. The...MD 20670 Dr. G. Hurst University of Pennsylvania Dr. Amos Freedy Wharton School Perceptronics, Inc. Philadelphia, PA 19174 6271 Variel Avenue

Multiple quantum criticality in a two-dimensional superconductor

NASA Astrophysics Data System (ADS)

Biscaras, J.; Bergeal, N.; Hurand, S.; Feuillet-Palma, C.; Rastogi, A.; Budhani, R. C.; Grilli, M.; Caprara, S.; Lesueur, J.

2013-06-01

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Multiple quantum criticality in a two-dimensional superconductor.

PubMed

Biscaras, J; Bergeal, N; Hurand, S; Feuillet-Palma, C; Rastogi, A; Budhani, R C; Grilli, M; Caprara, S; Lesueur, J

2013-06-01

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Density profiles of the exclusive queuing process

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Schadschneider, Andreas

2012-12-01

The exclusive queuing process (EQP) incorporates the exclusion principle into classic queuing models. It is characterized by, in addition to the entrance probability α and exit probability β, a third parameter: the hopping probability p. The EQP can be interpreted as an exclusion process of variable system length. Its phase diagram in the parameter space (α,β) is divided into a convergent phase and a divergent phase by a critical line which consists of a curved part and a straight part. Here we extend previous studies of this phase diagram. We identify subphases in the divergent phase, which can be distinguished by means of the shape of the density profile, and determine the velocity of the system length growth. This is done for EQPs with different update rules (parallel, backward sequential and continuous time). We also investigate the dynamics of the system length and the number of customers on the critical line. They are diffusive or subdiffusive with non-universal exponents that also depend on the update rules.

Universal patterns of equilibrium cluster growth in aqueous sugars observed by dynamic light scattering.

PubMed

Sidebottom, D L; Tran, Tri D

2010-11-01

Dynamic light scattering performed on aqueous solutions of three sugars (glucose, maltose and sucrose) reveal a common pattern of sugar cluster formation with a narrow cluster size distribution. In each case, equilibrium clusters form whose size increases with increasing sugar content in an identical power law manner in advance of a common, critical-like, percolation threshold near 83 wt % sugar. The critical exponent of the power law divergence of the cluster size varies with temperature, increasing with decreasing temperature, due to changes in the strength of the intermolecular hydrogen bond and appears to vanish for temperatures in excess of 90 °C. Detailed analysis of the cluster growth process suggests a two-stage process: an initial cluster phase formed at low volume fractions, ϕ, consisting of noninteracting, monodisperse sugar clusters whose size increases ϕ(1/3) followed by an aggregation stage, active at concentrations above about ϕ=40%, where cluster-cluster contact first occurs.

Algorithmic-Reducibility = Renormalization-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') Replacing CRUTCHES!!!: Gauss Modular/Clock-Arithmetic Congruences = Signal X Noise PRODUCTS..

NASA Astrophysics Data System (ADS)

Siegel, J.; Siegel, Edward Carl-Ludwig

2011-03-01

Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!

Gaussian free field in the background of correlated random clusters, formed by metallic nanoparticles

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, Jafar; Najafi, Morteza N.; Mohammadzadeh, Hossein

2018-05-01

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T - T c . The fractal dimension of iso-potential lines ( D f ), the exponent of the distribution function of the gyration radius ( τ r ), and the loop lengths ( τ l ), and also the exponent of the loop Green function x l change in terms of T - T c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D f ( T) - D f ( T c ) 1/√ ξ( T), in which ξ( T) is the spin correlation length in the Ising model.

Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the 'Standard Values'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogorelov, A. A.; Suslov, I. M.

2008-06-15

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standardmore » values and for a further increase in accuracy.« less

Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting

NASA Astrophysics Data System (ADS)

Chen, Leiming; Lee, Chiu Fan; Toner, John

2016-07-01

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.

Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting.

PubMed

Chen, Leiming; Lee, Chiu Fan; Toner, John

2016-07-25

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.

Anomalous elasticity, fluctuations and disorder in elastic membranes

NASA Astrophysics Data System (ADS)

Le Doussal, Pierre; Radzihovsky, Leo

2018-05-01

Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d → ∞, (ii) D → 4, and (iii) D = d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional (D = 2) membrane embedded in three dimensions (d = 3), we predict its universal roughness exponent ζ = 0 . 590, length-scale dependent elastic moduli exponents η = 0 . 821 and ηu = 0 . 358, and an anomalous Poisson ratio, σ = - 1 / 3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ‧ = 0 . 775 ,η‧ = 0 . 449, ηu‧ = 1 . 101 and a Poisson ratio σ‧ = - 1 / 3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a "phantom" sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν = 0 . 732 and η = 0 . 535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene.

Anomalous dimension in a two-species reaction-diffusion system

NASA Astrophysics Data System (ADS)

Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.

2018-01-01

We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \

Self-organized complexity in economics and finance

PubMed Central

Stanley, H. E.; Amaral, L. A. N.; Buldyrev, S. V.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.

2002-01-01

This article discusses some of the similarities between work being done by economists and by physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two newly discovered scaling results that appear to be universal, in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent −4 extending over 102 SDs (a factor of 108 on the y axis); this result is analogous to the Gutenberg–Richter power law describing the histogram of earthquakes of a given strength; and (ii) for a wide range of economic organizations, the histogram shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations. PMID:11875210

Hyperscaling breakdown and Ising spin glasses: The Binder cumulant

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2018-02-01

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.

Reversible island nucleation and growth with anomalous diffusion

NASA Astrophysics Data System (ADS)

Sabbar, Ehsan H.; Amar, Jacques G.

2017-10-01

Motivated by recent experiments on submonolayer organic film growth with anomalous diffusion, a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed (Amar and Semaan, 2016) [23], which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i = 1 with d = 2 . However, since many experiments correspond to a critical island-size larger than 1, it is of interest to determine if the RE predictions also hold in the case of reversible island nucleation with anomalous diffusion. Here we present the results of simulations of submonolayer growth with i = 2 (d = 2) which were carried out for both the case of superdiffusion (μ > 1) and subdiffusion (μ < 1) as well as for both ramified islands (df ≃ 2) and point-islands (df = ∞) . In the case of superdiffusion, corresponding to 'hot' freshly deposited monomers, excellent agreement is obtained with the predictions of the generalized RE theory for the exponents χ(μ) and χ1(μ) which describe the dependence of the island and monomer densities at fixed coverage on deposition rate F. In addition, the exponents do not depend on whether or not monomers remain superdiffusive or are thermalized (e.g. undergo regular diffusion) after detaching from a dimer. However, we also find that, as was previously found in the case of irreversible growth, the exponent χ only approaches its asymptotic value logarithmically with increasing 1/F. This result has important implications for the interpretation of experiments. Good agreement with the RE theory is also found in the case of subdiffusion for point-islands. However, in the case of ramified islands with subdiffusion and i = 2 , the exponents are significantly higher than predicted due to the fact that monomer capture dominates in the nucleation regime. A modified RE theory which takes this into account is presented, and excellent agreement is found with our simulations.

On the temperature derivative of the surface tension at a critical end point

NASA Astrophysics Data System (ADS)

Robert, M.; Tavan, P.

1983-03-01

It is shown that, according to the van der Waals theory of fluid interfaces, the surface tension of the interface between a This result holds for any number of phases and independently varying densities and is not restricted to classical values of the critical exponents.

Universities scale like cities.

PubMed

van Raan, Anthony F J

2013-01-01

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the 'gross university income' in terms of total number of citations over 'size' in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities--the top-100 European universities--we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.

Heat Capacity Anomaly Near the Lower Critical Consolute Point of Triethylamine-Water

NASA Technical Reports Server (NTRS)

Flewelling, Anne C.; DeFonseka, Rohan J.; Khaleeli, Nikfar; Partee, J.; Jacobs, D. T.

1996-01-01

The heat capacity of the binary liquid mixture triethylamine-water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent a was determined to be 0.107 +/- 0.006, consistent with theoretical predictions. When alpha was fixed at 0.11 to determine various amplitudes consistently, our values of A(+) and A(-) agreed with a previous heat capacity measurement, but the value of A(-) was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A(+)/ A(-) = 0.56 +/- 0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid-vapor systems. The correction to scaling amplitude ratio D(+)/D(-) = 0.5 +/- 0.1 was half of that predicted. As a result of several more precise theoretical calculations and experimental determinations, the two-scale-factor universality ratio X, which we found to be 0.019 +/- 0.003, now is consistent among experiments and theories. A new 'universal' amplitude ratio R(sup +/-)(sub Bcr) involving the amplitudes for the specific heat was tested. Our determination of R(sup +/-)(sub Bcr) = -0.5 +/- 0.1 and R(sup -)(sub Bcr) = 1.1 +/- 0.1 is smaller in magnitude than predicted and is the first such determination in a binary fluid mixture.

Critical behaviour and filed dependence of magnetic entropy change in K-doped manganites Pr0.8Na0.2-xKxMnO3 (x = 0.10 and 0.15)

NASA Astrophysics Data System (ADS)

Ben Khlifa, H.; M'nassri, R.; Tarhouni, S.; Regaieg, Y.; Cheikhrouhou-Koubaa, W.; Chniba-Boudjada, N.; Cheikhrouhou, A.

2018-01-01

The orthorhombic Pr0.8Na0.2-xKxMnO3 (x = 0.10 and 0.15) manganites are prepared by using the solid state reaction at high temperatures. The critical exponents (β, γ, δ) are investigated through various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis based on the data of the magnetic measurements recorded around the Curie temperature. The critical exponents are derived from the magnetization data using the Kouvel-Fisher method, are found to be β = 0.32(4) and γ = 1.29(2) at TC 123 K for x = 0.10 and β = 0.31(1) and γ = 1.25(2) at TC 133 K for x = 0.15. The critical exponent values obtained for both samples are comparable to the values predicted by the 3D-Ising model, and have also been verified by the scaling equation of state. Such results demonstrate the existence of ferromagnetic short-range order in our materials. The magnetic entropy changes of polycrystalline samples with a second-order phase transition are investigated. A large magnetic entropy change deduced from isothermal magnetization curves, is observed in our samples with a peak centered on their respective Curie temperatures (TC). The field dependence of the magnetic entropy changes are analyzed, which show power law dependence ΔSmax ≈ a(μ0 H) n at transition temperature. The values of n obey to the Curie Weiss law above the transition temperature. It is shown that for the investigated materials, the magnetic entropy change follow a master curve behaviour. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve for both samples.

Role of fluctuations in random compressible systems at marginal dimensionality

NASA Astrophysics Data System (ADS)

Meissner, G.; Sasvári, L.; Tadić, B.

1986-07-01

In a unified treatment we have studied the role of fluctuations in uniaxial random systems at marginal dimensionality d*=4 with the n=1 component order parameter being coupled to elastic degrees of freedom. Depending on the ratio of the nonuniversal parameters of quenched disorder Δ0 and of elastic fluctuations v~0, a first- or second-order phase transition is found to occur, separated by a tricritical point. A complete account of critical properties and of macroscopic as well as of microscopic elastic stability is given for temperatures T>Tc. Universal singularities of thermodynamic functions are determined for t=(T-Tc)/Tc-->0 including the tricritical point: for v~0/Δ0>-2, they are the same as in a rigid random system; for v~0/Δ0=-2, they are different due to lattice compressibility being related, however, to the former by Fisher renormalization. Fluctuation corrections in one-loop approximation have been evaluated in a nonuniversal critical temperature range, tx<

Critical scaling of a jammed system after a quench of temperature.

PubMed

Otsuki, Michio; Hayakawa, Hisao

2012-09-01

Critical behavior of soft repulsive particles after quench of temperature near the jamming transition is numerically investigated. It is found that the plateau of the mean-square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.

Dynamical correlation functions of the quadratic coupling spin-Boson model

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions {C}O(ω ), with the operator \\hat{O} taken as {\\hat{{{σ }}}}x, {\\hat{{{σ }}}}z, and \\hat{X}, respectively. In the weak-coupling regime α < {α }{{c}}, these functions show power law ω-dependence in the small frequency limit, with the powers 1+2s, 1+2s, and s, respectively. At the critical point α ={α }{{c}} of the boson-unstable quantum phase transition, the critical exponents y O of these correlation functions are obtained as {y}{{{σ }}x}={y}{{{σ }}z}=1-2s and {y}X=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of {C}{{{σ }}x}(ω ) is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point. Project supported by the National Key Basic Research Program of China (Grant No. 2012CB921704), the National Natural Science Foundation of China (Grant No. 11374362), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 15XNLQ03).

Anomalous transport in Charney-Hasegawa-Mima flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leoncini, Xavier; Agullo, Olivier; Benkadda, Sadruddin

2005-08-01

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around {mu}=1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law {gamma}={mu}+1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero ofmore » the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.« less

Short-Time Dynamics of the Random n-Vector Model

NASA Astrophysics Data System (ADS)

Chen, Yuan; Li, Zhi-Bing; Fang, Hai; He, Shun-Shan; Situ, Shu-Ping

2001-11-01

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach. Asymptotic scaling laws are studied in a frame of the expansion in ɛ=4-d for n≠1 and {√ɛ} for n=1 respectively. In d<4, the initial slip exponents θ‧ for the order parameter and θ for the response function are calculated up to the second order in ɛ=4-d for n≠1 and {√ɛ} for n=1 at the random fixed point respectively. Our results show that the random impurities exert a strong influence on the short-time dynamics for d<4 and n

Phase diagram, correlation gap, and critical properties of the coulomb glass.

PubMed

Goethe, Martin; Palassini, Matteo

2009-07-24

We investigate the lattice Coulomb glass model in three dimensions via Monte Carlo simulations. No evidence for an equilibrium glass phase is found down to very low temperatures, although the correlation length increases rapidly near T = 0. A charge-ordered phase exists at low disorder. The transition to this phase is consistent with the random field Ising universality class, which shows that the interaction is effectively screened at moderate temperature. For large disorder, the single-particle density of states near the Coulomb gap satisfies the scaling relation g(epsilon, T) = T;{delta}f(|epsilon|/T) with delta = 2.01 +/- 0.05 in agreement with the prediction of Efros and Shklovskii. For decreasing disorder, a crossover to a larger effective exponent occurs due to the proximity of the charge-ordered phase.

Solving the flatness problem with an anisotropic instanton in Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Bramberger, Sebastian F.; Coates, Andrew; Magueijo, João; Mukohyama, Shinji; Namba, Ryo; Watanabe, Yota

2018-02-01

In Hořava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called "anisotropic scaling," with the dynamical critical exponent z =3 , lies at the base of its renormalizability. This scaling also leads to a novel mechanism of generating scale-invariant cosmological perturbations, solving the horizon problem without inflation. In this paper we propose a possible solution to the flatness problem, in which we assume that the initial condition of the Universe is set by a small instanton respecting the same scaling. We argue that the mechanism may be more general than the concrete model presented here. We rely simply on the deformed dispersion relations of the theory, and on equipartition of the various forms of energy at the starting point.

Magnetism of internal surfaces in a fractal structure

NASA Astrophysics Data System (ADS)

Branco, N. S.; Chame, Anna

1993-09-01

We study the inhomogeneous magnetization behavior of an Ising ferromagnet in Sierpiński pastry shells, using a real-space renormalization group approach. Two qualitatively different regions on the fractal are distinguished: the bulk and the set of internal surfaces which border the eliminated portions. We obtain the spontaneous mean magnetizations for these regions as a function of the temperature for different values of α = JS/ JB (J S and J B are the internal surface and bulk coupling constants respectively) and different geometrical parameters b and l. The critical β exponents are obtained for the several transitions. We obtain different universality classes for the bulk transitions, depending on what occurs at the surfaces, and a step-like behavior of the magnetization as a function of the temperature of some values of b and l.

Simulating statistics of lightning-induced and man made fires

NASA Astrophysics Data System (ADS)

Krenn, R.; Hergarten, S.

2009-04-01

The frequency-area distributions of forest fires show power-law behavior with scaling exponents α in a quite narrow range, relating wildfire research to the theoretical framework of self-organized criticality. Examples of self-organized critical behavior can be found in computer simulations of simple cellular automata. The established self-organized critical Drossel-Schwabl forest fire model (DS-FFM) is one of the most widespread models in this context. Despite its qualitative agreement with event-size statistics from nature, its applicability is still questioned. Apart from general concerns that the DS-FFM apparently oversimplifies the complex nature of forest dynamics, it significantly overestimates the frequency of large fires. We present a straightforward modification of the model rules that increases the scaling exponent α by approximately 1•3 and brings the simulated event-size statistics close to those observed in nature. In addition, combined simulations of both the original and the modified model predict a dependence of the overall distribution on the ratio of lightning induced and man made fires as well as a difference between their respective event-size statistics. The increase of the scaling exponent with decreasing lightning probability as well as the splitting of the partial distributions are confirmed by the analysis of the Canadian Large Fire Database. As a consequence, lightning induced and man made forest fires cannot be treated separately in wildfire modeling, hazard assessment and forest management.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grebogi, C.; Yorke, J.A.

This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)

The origin of the criticality in meme popularity distribution on complex networks.

PubMed

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-24

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

The origin of the criticality in meme popularity distribution on complex networks

PubMed Central

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-01-01

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks. PMID:27009399

The origin of the criticality in meme popularity distribution on complex networks

NASA Astrophysics Data System (ADS)

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-01

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

Fractal dimension, walk dimension and conductivity exponent of karst networks around Tulum.

NASA Astrophysics Data System (ADS)

Hendrick, Martin; Renard, Philippe

2016-06-01

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension d_f, conductivity exponent ˜{μ} and walk dimension d_w are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: d_f≈ 1.5, d_w≈ 2.4, ˜{μ}≈ 0.9. We observe that the Einstein relation holds for these structures ˜{μ} ≈ -d_f + d_w. These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann method: Massive scalar theory and critical exponents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, Paulo R. S.; Leite, Marcelo M.

2013-09-15

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar λφ{sup 4} theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents η and ν at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann (BPHZ) method at the same loop order,more » show that the proposed method requires fewer diagrams and establish a connection between the two approaches.« less

Coherent Anomaly Method Calculation on the Cluster Variation Method. II.

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

The critical exponents of the bond percolation model are calculated in the D(= 2,3,…)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Fragmentation scaling of percolation clusters in two and three dimensions: Large-cell Monte Carlo RG approach

NASA Astrophysics Data System (ADS)

Cheon, M.; Chang, I.

1999-04-01

The scaling behavior for a binary fragmentation of critical percolation clusters is investigated by a large-cell Monte Carlo real-space renormalization group method in two and three dimensions. We obtain accurate values of critical exponents λ and phi describing the scaling of fragmentation rate and the distribution of fragments' masses produced by a binary fragmentation. Our results for λ and phi show that the fragmentation rate is proportional to the size of mother cluster, and the scaling relation σ = 1 + λ - phi conjectured by Edwards et al. to be valid for all dimensions is satisfied in two and three dimensions, where σ is the crossover exponent of the average cluster number in percolation theory, which excludes the other scaling relations.

Critical exponents for diluted resistor networks

NASA Astrophysics Data System (ADS)

Stenull, O.; Janssen, H. K.; Oerding, K.

1999-05-01

An approach by Stephen [Phys. Rev. B 17, 4444 (1978)] is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky [Phys. Rev. B 35, 6964 (1987)]. By a decomposition of the principal Feynman diagrams, we obtain diagrams which again can be interpreted as resistor networks. This interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent φ up to second order in ɛ=6-d, where d is the spatial dimension. Our result φ=1+ɛ/42+4ɛ2/3087 verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts-model formulation of the random resistor network.

Polymer translocation through a nanopore: a showcase of anomalous diffusion.

PubMed

Milchev, A; Dubbeldam, Johan L A; Rostiashvili, Vakhtang G; Vilgis, Thomas A

2009-04-01

We investigate the translocation dynamics of a polymer chain threaded through a membrane nanopore by a chemical potential gradient that acts on the chain segments inside the pore. By means of diverse methods (scaling theory, fractional calculus, and Monte Carlo and molecular dynamics simulations), we demonstrate that the relevant dynamic variable, the transported number of polymer segments, s(t), displays an anomalous diffusive behavior, both with and without an external driving force being present. We show that in the absence of drag force the time tau, needed for a macromolecule of length N to thread from the cis into the trans side of a cell membrane, scales as tauN(2/alpha) with the chain length. The anomalous dynamics of the translocation process is governed by a universal exponent alpha= 2/(2nu + 2 - gamma(1)), which contains the basic universal exponents of polymer physics, nu (the Flory exponent) and gamma(1) (the surface entropic exponent). A closed analytic expression for the probability to find s translocated segments at time t in terms of chain length N and applied drag force f is derived from the fractional Fokker-Planck equation, and shown to provide analytic results for the time variation of the statistical moments and . It turns out that the average translocation time scales as tau proportional, f(-1)N(2/alpha-1). These results are tested and found to be in perfect agreement with extensive Monte Carlo and molecular dynamics computer simulations.

Revealing mesoscopic structural universality with diffusion.

PubMed

Novikov, Dmitry S; Jensen, Jens H; Helpern, Joseph A; Fieremans, Els

2014-04-08

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.

Variational Approach to Monte Carlo Renormalization Group

NASA Astrophysics Data System (ADS)

Wu, Yantao; Car, Roberto

2017-12-01

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Quantum spin chains with multiple dynamics

NASA Astrophysics Data System (ADS)

Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William

2017-11-01

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤z <2.7 , which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.

Bootstrap percolation on spatial networks

NASA Astrophysics Data System (ADS)

Gao, Jian; Zhou, Tao; Hu, Yanqing

2015-10-01

Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.

Global asymmetry of fluids and local singularity in the diameter of the coexistence curve.

PubMed

Rogankov, Vitaly B; Levchenko, Valeriy I

2013-05-01

By combining a measurable vapor-liquid coexistence curve and the extended van der Waals-type of equation of state (EOS) with the additional temperature-dependent coefficient, the phenomenological model of global fluid asymmetry has been developed separately for both coexisting bulk phases in the entire range of subcritical states. It is shown, in particular, that the adequate description of a liquid branch and its near-critical vicinity in terms of appropriate critical exponents and amplitudes connected by the two-scale-factor universal interrelations can be achieved. The asymmetric influence of heterophase fluctuations on the criticality of gaseous states is demonstrated. It is inherently similar to the well-known Fisher's droplet model, which corresponds to the scaling EOS too. The principle of corresponding isotherms has been formulated without any adjustable parameters. An attempt to avoid the use of a locally singular coexistence-curve diameter is proposed in the framework of two alternative models. The accurate vapor-liquid data for two fluid metals, Rb and Cs, as well as two molecular fluids, C(2)H(6) and CO(2), are reanalyzed by the above models to confirm the presumed opportunity.

Critical exponent analysis of lightly germanium-doped La0.7Ca0.3Mn1-xGexO3 (x = 0.05 and x = 0.07)

NASA Astrophysics Data System (ADS)

Nanto, Dwi; Kurniawan, Budhy; Soegijono, Bambang; Ghosh, Nilotpal; Hwang, Jong-Soon; Yu, Seong-Cho

2018-04-01

We have used a critical behavior study of La0.7Ca0.3MnO3 (LCMO) manganite perovskites whose Mn sites have been doped with Ge to explore magnetic interactions. Light Ge doping of 5 or 7 percent tended to produce LCMOs with second order magnetic transitions. The critical parameters of 5- and 7-percent Ge-doped LCMO were determined to be TC = 185 K, β = 0.331 ± 0.019, and γ = 1.15 ± 0.017; and TC = 153 K, β = 0.496 ± 0.011, and γ = 1.03 ± 0.046, respectively, via the modified Arrott plot method. Isothermal magnetization data collected near the Curie temperature (TC) was split into a universal function with two branches M(H,ɛ) = |ɛ|βf±(H/|ɛ|β+γ), where ɛ=(T-TC)/TC is the reduced temperature. f+ is used when T>TC, while f̲ is used when T

Scale invariance and universality in economic phenomena

NASA Astrophysics Data System (ADS)

Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.

2002-03-01

This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly discovered scaling results that appear to be `universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behaviour of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious `symmetry breaking' for values of Σ above a certain threshold value Σc here Σ is defined to be the local first moment of the probability distribution of demand Ω - the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behaviour of the probability density of the magnetization for fixed values of the inverse temperature.

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

NASA Astrophysics Data System (ADS)

Lee, Hyun-Jung; Kim, Ki-Seok

2018-04-01

We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the multifractality singular spectrum can be classified into two categories, confirming the appearance of two types of mobility edges.

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

Universities Scale Like Cities

PubMed Central

van Raan, Anthony F. J.

2013-01-01

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the ‘gross university income’ in terms of total number of citations over ‘size’ in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities -the top-100 European universities- we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment. PMID:23544062

Statistical properties of world investment networks

NASA Astrophysics Data System (ADS)

Song, Dong-Ming; Jiang, Zhi-Qiang; Zhou, Wei-Xing

2009-06-01

We have performed a detailed investigation on the world investment networks constructed from the Coordinated Portfolio Investment Survey (CPIS) data of the International Monetary Fund, ranging from 2001 to 2006. The distributions of degrees and node strengths are scale-free. The weight distributions can be well modeled by the Weibull distribution. The maximum flow spanning trees of the world investment networks possess two universal allometric scaling relations, independent of time and the investment type. The topological scaling exponent is 1.17±0.02 and the flow scaling exponent is 1.03±0.01.

Anomalous charge storage exponents of organic bulk heterojunction solar cells.

NASA Astrophysics Data System (ADS)

Nair, Pradeep; Dwivedi, Raaz; Kumar, Goutam; Dept of Electrical Engineering, IIT Bombay Team

2013-03-01

Organic bulk heterojunction (BHJ) devices are increasingly being researched for low cost solar energy conversion. The efficiency of such solar cells is dictated by various recombination processes involved. While it is well known that the ideality factor and hence the charge storage exponents of conventional PN junction diodes are influenced by the recombination processes, the same aspects are not so well understood for organic solar cells. While dark currents of such devices typically show an ideality factor of 1 (after correcting for shunt resistance effects, if any), surprisingly, a wide range of charge storage exponents for such devices are reported in literature alluding to apparent concentration dependence for bi-molecular recombination rates. In this manuscript we critically analyze the role of bi-molecular recombination processes on charge storage exponents of organic solar cells. Our results indicate that the charge storage exponents are fundamentally influenced by the electrostatics and recombination processes and can be correlated to the dark current ideality factors. We believe that our findings are novel, and advance the state-of the art understanding on various recombination processes that dictate the performance limits of organic solar cells. The authors would like to thank the Centre of Excellence in Nanoelectronics (CEN) and the National Centre for Photovoltaic Research and Education (NCPRE), IIT Bombay for computational and financial support

Scaling tunable network model to reproduce the density-driven superlinear relation

NASA Astrophysics Data System (ADS)

Gao, Liang; Shan, Xiaoya; Qin, Yuhao; Yu, Senbin; Xu, Lida; Gao, Zi-You

2018-03-01

Previous works have shown the universality of allometric scaling under total and density values at the city level, but our understanding of the size effects of regions on the universality of allometric scaling remains inadequate. Here, we revisit the scaling relations between the gross domestic production (GDP) and the population based on the total and density values and first reveal that the allometric scaling under density values for different regions is universal. The scaling exponent β under the density value is in the range of (1.0, 2.0], which unexpectedly exceeds the range observed by Pan et al. [Nat. Commun. 4, 1961 (2013)]. For the wider range, we propose a network model based on a 2D lattice space with the spatial correlation factor α as a parameter. Numerical experiments prove that the generated scaling exponent β in our model is fully tunable by the spatial correlation factor α. Our model will furnish a general platform for extensive urban and regional studies.

On the power law of passive scalars in turbulence

NASA Astrophysics Data System (ADS)

Gotoh, Toshiyuki; Watanabe, Takeshi

2015-11-01

It has long been considered that the moments of the scalar increment with separation distance r obey power law with scaling exponents in the inertial convective range and the exponents are insensitive to variation of pumping of scalar fluctuations at large scales, thus the scaling exponents are universal. We examine the scaling behavior of the moments of increments of passive scalars 1 and 2 by using DNS up to the grid points of 40963. They are simultaneously convected by the same isotropic steady turbulence atRλ = 805 , but excited by two different methods. Scalar 1 is excited by the random scalar injection which is isotropic, Gaussian and white in time at law wavenumber band, while Scalar 2 is excited by the uniform mean scalar gradient. It is found that the local scaling exponents of the scalar 1 has a logarithmic correction, meaning that the moments of the scalar 1 do not obey simple power law. On the other hand, the moments of the scalar 2 is found to obey the well developed power law with exponents consistent with those in the literature. Physical reasons for the difference are explored. Grants-in-Aid for Scientific Research 15H02218 and 26420106, NIFS14KNSS050, HPCI project hp150088 and hp140024, JHPCN project jh150012.

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

NASA Astrophysics Data System (ADS)

Bera, Anindita; Mishra, Utkarsh; Singha Roy, Sudipto; Biswas, Anindya; Sen(De), Aditi; Sen, Ujjwal

2018-06-01

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.

Entanglement entropy for the long-range Ising chain in a transverse field.

PubMed

Koffel, Thomas; Lewenstein, M; Tagliacozzo, Luca

2012-12-28

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.

Critical behavior of the ideal-gas Bose-Einstein condensation in the Apollonian network.

PubMed

de Oliveira, I N; dos Santos, T B; de Moura, F A B F; Lyra, M L; Serva, M

2013-08-01

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension d(s)=2ln(3)/ln(9/5)~/=3.74.

Superlinear scaling of offspring at criticality in branching processes

NASA Astrophysics Data System (ADS)

Saichev, A.; Sornette, D.

2014-01-01

For any branching process, we demonstrate that the typical total number rmp(ντ) of events triggered over all generations within any sufficiently large time window τ exhibits, at criticality, a superlinear dependence rmp(ντ)˜(ντ)γ (with γ >1) on the total number ντ of the immigrants arriving at the Poisson rate ν. In branching processes in which immigrants (or sources) are characterized by fertilities distributed according to an asymptotic power-law tail with tail exponent 1<γ ⩽2, the exponent of the superlinear law for rmp(ντ) is identical to the exponent γ of the distribution of fertilities. For γ >2 and for standard branching processes without power-law distribution of fertilities, rmp(ντ)˜(ντ)2. This scaling law replaces and tames the divergence ντ /(1-n) of the mean total number R¯t(τ) of events, as the branching ratio (defined as the average number of triggered events of first generation per source) tends to 1. The derivation uses the formalism of generating probability functions. The corresponding prediction is confirmed by numerical calculations, and an heuristic derivation enlightens its underlying mechanism. We also show that R¯t(τ) is always linear in ντ even at criticality (n =1). Our results thus illustrate the fundamental difference between the mean total number, which is controlled by a few extremely rare realizations, and the typical behavior represented by rmp(ντ).

Interfacial properties in a discrete model for tumor growth

NASA Astrophysics Data System (ADS)

Moglia, Belén; Guisoni, Nara; Albano, Ezequiel V.

2013-03-01

We propose and study, by means of Monte Carlo numerical simulations, a minimal discrete model for avascular tumor growth, which can also be applied for the description of cell cultures in vitro. The interface of the tumor is self-affine and its width can be characterized by the following exponents: (i) the growth exponent β=0.32(2) that governs the early time regime, (ii) the roughness exponent α=0.49(2) related to the fluctuations in the stationary regime, and (iii) the dynamic exponent z=α/β≃1.49(2), which measures the propagation of correlations in the direction parallel to the interface, e.g., ξ∝t1/z, where ξ is the parallel correlation length. Therefore, the interface belongs to the Kardar-Parisi-Zhang universality class, in agreement with recent experiments of cell cultures in vitro. Furthermore, density profiles of the growing cells are rationalized in terms of traveling waves that are solutions of the Fisher-Kolmogorov equation. In this way, we achieved excellent agreement between the simulation results of the discrete model and the continuous description of the growth front of the culture or tumor.

Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

NASA Astrophysics Data System (ADS)

Hong, Hyunsuk

2017-07-01

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984), 10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν ¯=5 /4 . Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ =1 /4 , which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007), 10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν ¯=5 /2 . On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν ¯=5 /4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

Quasiperiodic Quantum Ising Transitions in 1D

NASA Astrophysics Data System (ADS)

Crowley, P. J. D.; Chandran, A.; Laumann, C. R.

2018-04-01

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν =1+ (exact) and z ≈1.9 , Δσ≈0.16 , and Δγ≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.

Nonequilibrium phase transition in a self-activated biological network.

PubMed

Berry, Hugues

2003-03-01

We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.

Phase order in superfluid helium films

NASA Astrophysics Data System (ADS)

Bramwell, Steven T.; Faulkner, Michael F.; Holdsworth, Peter C. W.; Taroni, Andrea

2015-12-01

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent β = 3 π^2/128 , a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids. This paper is dedicated to the memory of our friend and colleague Maxime Clusel, with whom we enjoyed many stimulating discussions on related topics.

Emergence and Phase Transitions

NASA Astrophysics Data System (ADS)

Sikkema, Arnold

2006-05-01

Phase transitions are well defined in physics through concepts such as spontaneous symmetry breaking, order parameter, entropy, and critical exponents. But emergence --- also exhibiting whole-part relations (such as top-down influence), unpredictability, and insensitivity to microscopic detail --- is a loosely-defined concept being used in many disciplines, particularly in psychology, biology, philosophy, as well as in physics[1,2]. I will review the concepts of emergence as used in the various fields and consider the extent to which the methods of phase transitions can clarify the usefulness of the concept of emergence both within the discipline of physics and beyond.1. Robert B. Laughlin, A Different Universe: Reinventing Physics from the Bottom Down (New York: Basic Books, 2005). 2. George F.R. Ellis, ``Physics and the Real World'', Physics Today, vol. 58, no. 7 (July 2005) pp. 49-54.

Magnetic order and spin dynamics in La2O2Fe2OSe2 probed by 57Fe Mössbauer, 139La NMR, and muon-spin relaxation spectroscopy

NASA Astrophysics Data System (ADS)

Günther, M.; Kamusella, S.; Sarkar, R.; Goltz, T.; Luetkens, H.; Pascua, G.; Do, S.-H.; Choi, K.-Y.; Zhou, H. D.; Blum, C. G. F.; Wurmehl, S.; Büchner, B.; Klauss, H.-H.

2014-11-01

We present a detailed local probe study of the magnetic order in the oxychalcogenide La2O2Fe2OSe2 utilizing 57Fe Mössbauer, 139La NMR, and muon-spin relaxation spectroscopy. This system can be regarded as an insulating reference system of the Fe arsenide and chalcogenide superconductors. From the combination of the local probe techniques we identify a noncollinear magnetic structure similar to Sr2F2Fe2OS2 . The analysis of the magnetic order parameter yields an ordering temperature TN=90.1 K and a critical exponent of β =0.133 , which is close to the two-dimensional Ising universality class as reported in the related oxychalcogenide family.

Revealing mesoscopic structural universality with diffusion

PubMed Central

Novikov, Dmitry S.; Jensen, Jens H.; Helpern, Joseph A.; Fieremans, Els

2014-01-01

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke. PMID:24706873

Temperature, concentration, and frequency dependence of the dielectric constant near the critical point of the binary liquid mixture nitrobenzene-tetradecane

NASA Astrophysics Data System (ADS)

Leys, Jan; Losada-Pérez, Patricia; Cordoyiannis, George; Cerdeiriña, Claudio A.; Glorieux, Christ; Thoen, Jan

2010-03-01

Detailed results are reported for the dielectric constant ɛ as a function of temperature, concentration, and frequency near the upper critical point of the binary liquid mixture nitrobenzene-tetradecane. The data have been analyzed in the context of the recently developed concept of complete scaling. It is shown that the amplitude of the low frequency critical Maxwell-Wagner relaxation (with a relaxation frequency around 10 kHz) along the critical isopleth is consistent with the predictions of a droplet model for the critical fluctuations. The temperature dependence of ɛ in the homogeneous phase can be well described with a combination of a (1-α) power law term (with α the heat capacity critical exponent) and a linear term in reduced temperature with the Ising value for α. For the proper description of the temperature dependence of the difference Δɛ between the two coexisting phases below the critical temperature, it turned out that good fits with the Ising value for the order parameter exponent β required the addition of a corrections-to-scaling contribution or a linear term in reduced temperature. Good fits to the dielectric diameter ɛd require a (1-α) power law term, a 2β power law term (in the past considered as spurious), and a linear term in reduced temperature, consistent with complete scaling.

Cook-Levin Theorem Algorithmic-Reducibility/Completeness = Wilson Renormalization-(Semi)-Group Fixed-Points; ``Noise''-Induced Phase-Transitions (NITs) to Accelerate Algorithmics (``NIT-Picking'') REPLACING CRUTCHES!!!: Models: Turing-machine, finite-state-models, finite-automata

NASA Astrophysics Data System (ADS)

Young, Frederic; Siegel, Edward

Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!

Exact determination of asymptotic CMB temperature-redshift relation

NASA Astrophysics Data System (ADS)

Hahn, Steffen; Hofmann, Ralf

2018-02-01

Based on energy conservation in a Friedmann-Lemaître-Robertson-Walker (FLRW) Universe, on the Legendre transformation between energy density and pressure, and on nonperturbative asymptotic freedom at high temperatures, we derive the coefficient νCMB in the high-temperature (T) — redshift (z) relation, T/T0 = νCMB(z + 1), of the Cosmic Microwave Background (CMB). Theoretically, our calculation relies on a deconfining SU(2) rather than a U(1) photon gas. We prove that νCMB = (1/4)1/3 = 0.629960(5), representing a topological invariant. Interestingly, the relative deviation of νCMB from the critical exponent associated with the correlation length l of the 3D Ising model, νIsing = 0.629971(4), is less than 2 × 10-5. We are not in a position to establish a direct theoretical link between νCMB and νIsing as suggested by the topological nature of νCMB and the fact that both theories are members of the same universality class. We do, however, spell out a somewhat speculative, strictly monotonic map from the physical Ising temperature 𝜃 to a fictitious SU(2) Yang-Mills temperature T, the latter continuing the asymptotic dependence of the scale factor a on T/T0 for T/T0 ≫ 1 down to T = 0, and we identify an exponential map from a to l to reproduce critical Ising behavior.

Regulator dependence of fixed points in quantum Einstein gravity with R 2 truncation

NASA Astrophysics Data System (ADS)

Nagy, S.; Fazekas, B.; Peli, Z.; Sailer, K.; Steib, I.

2018-03-01

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the R 2 term.

Avalanche statistics from data with low time resolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

LeBlanc, Michael; Nawano, Aya; Wright, Wendelin J.

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distributionmore » of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.« less

Observations in Fracture Toughness Testing of Glasses and Optical Ceramics

NASA Technical Reports Server (NTRS)

Salem, Jon

2017-01-01

Fracture toughness is a critical structural design parameter and an excellent metrics to rank materials. Itdetermines fracture strength by way of the flaws, both inherent and induced, and defines the endpoint of the slow crackgrowth curve. The fracture toughness of structural and optical ceramics, and glasses as measured by several techniques is compared. When good metrology is employed, the results are very comparable with two exceptions: materials exhibiting crack growth resistance and those with a low SCG exponents. For materials with R-curves, the result is a function of extension and can be minimized with short cracks. For materials with low SCG exponents, such as glasses, elimination of the corrosive media andor increasing the stress intensity rate minimizes effects. A summary of values is given, and it appears that highly modified glasses exhibit lower fracture toughness and slow crack growth exponent than high purity glasses such as fused silica.

Avalanche statistics from data with low time resolution

DOE PAGES

LeBlanc, Michael; Nawano, Aya; Wright, Wendelin J.; ...

2016-11-22

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distributionmore » of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.« less

Scientific Objectives of the Critical Viscosity Experiment

NASA Technical Reports Server (NTRS)

Berg, R. F.; Moldover, M. R.

1993-01-01

In microgravity, the Critical Viscosity Experiment will measure the viscosity of xenon 15 times closer to the critical point than is possible on earth. The results are expected to include the first direct observation of the predicted power-law divergence of viscosity in a pure fluid and they will test calculations of the value of the exponent associated with the divergence. The results, when combined with Zeno's decay-rate data, will strengthen the test of mode coupling theory. Without microgravity viscosity data, the Zeno test will require an extrapolation of existing 1-g viscosity data by as much as factor of 100 in reduced temperature. By necessity, the extrapolation would use an incompletely verified theory of viscosity crossover. With the microgravity viscosity data, the reliance on crossover models will be negligible allowing a more reliable extrapolation. During the past year, new theoretical calculations for the viscosity exponent finally achieved consistency with the best experimental data for pure fluids. This report gives the justification for the proposed microgravity Critical Viscosity Experiment in this new context. This report also combines for the first time the best available light scattering data with our recent viscosity data to demonstrate the current status of tests of mode coupling theory.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; de Candia, Antonio; Scarpetta, Silvia

2016-07-01

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-order one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Effect of long-range interactions on the phase transition of Axelrod's model

NASA Astrophysics Data System (ADS)

Reia, Sandro M.; Fontanari, José F.

2016-11-01

Axelrod's model with F =2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q , exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite-size scaling to study the critical behavior of the order parameter ρ , which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ ˜(qc0-q )β with β ≈0.25 at the critical point qc0≈3.10 and that the exponent that measures the width of the critical region is ν0≈2.1 . In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point qcp increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent νp≈1 for p >0 , increases with the square root of the number of nodes of the resulting small-world network.

Static critical behavior of the q-states Potts model: High-resolution entropic study

NASA Astrophysics Data System (ADS)

Caparica, A. A.; Leão, Salviano A.; DaSilva, Claudio J.

2015-11-01

Here we report a precise computer simulation study of the static critical properties of the two-dimensional q-states Potts model using very accurate data obtained from a modified Wang-Landau (WL) scheme proposed by Caparica and Cunha-Netto (2012). This algorithm is an extension of the conventional WL sampling, but the authors changed the criterion to update the density of states during the random walk and established a new procedure to windup the simulation run. These few changes have allowed a more precise microcanonical averaging which is essential to a reliable finite-size scaling analysis. In this work we used this new technique to determine the static critical exponents β, γ, and ν, in an unambiguous fashion. The static critical exponents were determined as β = 0.10811(77) , γ = 1.4459(31) , and ν = 0.8197(17) , for the q = 3 case, and β = 0.0877(37) , γ = 1.3161(69) , and ν = 0.7076(10) , for the q = 4 Potts model. A comparison of the present results with conjectured values and with those obtained from other well established approaches strengthens this new way of performing WL simulations.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: ludovico.minati@ifj.edu; Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków; Candia, Antonio de

2016-07-15

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-ordermore » one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.« less

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-Dimensional Dirac Semimetals.

PubMed

Fu, Bo; Zhu, Wei; Shi, Qinwei; Li, Qunxiang; Yang, Jinlong; Zhang, Zhenyu

2017-04-07

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behavior is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. We further show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-dimensional Dirac Semimetals

DOE PAGES

Fu, Bo; Zhu, Wei; Shi, Qinwei; ...

2017-04-03

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behaviormore » is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. Furthermore, we show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.« less

On projectile fragmentation at high-velocity perforation of a thin bumper

NASA Astrophysics Data System (ADS)

Myagkov, N. N.; Stepanov, V. V.

2014-09-01

By means of 3D numerical simulations, we study the statistical properties of the fragments cloud formed during high-velocity impact of a spherical projectile on a mesh bumper. We present a quantitative description of the projectile fragmentation, and study the nature of the transition from the damage to the fragmentation of the projectile when the impact velocity varies. A distinctive feature of the present work is that the calculations are carried out by smoothed particle hydrodynamics (SPH) method applied to the equations of mechanics of deformable solids (MDS). We describe the materials behavior by the Mie-Grüneisen equation of state and the Johnson-Cook model for the yield strength. The maximum principal stress spall model is used as the fracture model. It is shown that the simulation results of fragmentation based on the MDS equations by the SPH method are qualitatively consistent with the results obtained earlier on the basis of the molecular dynamics and discrete element models. It is found that the power-law distribution exponent does not depend on energy imparted to the projectile during the high-velocity impact. At the same time, our calculations show that the critical impact velocity, the power-law exponent and other critical exponents depend on the fracture criterion.

Superconductor-insulator transition on annealed complex networks.

PubMed

Bianconi, Ginestra

2012-06-01

Cuprates show multiphase and multiscale complexity that has hindered physicists search for the mechanism of high T{c} for many years. Recently the interest has been addressed to a possible optimum inhomogeneity of dopants, defects, and interstitials, and the structural scale invariance of dopants detected by scanning micro-x-ray diffraction has been reported to promote the critical temperature. In order to shed light on critical phenomena on granular materials, here we propose a stylized model capturing the essential characteristics of the superconducting-insulator transition of a highly dynamical, heterogeneous granular material: the random transverse Ising model (RTIM) on annealed complex network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power-law distribution, the critical temperature for the onset of the superconducting phase diverges to infinity as the power-law exponent γ of the expected degree distribution is less than 3, i.e., γ<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power-law expected degree distribution characterized by an exponent γ. We find that for g=g{c} the critical temperature for the superconducting-insulator transition has a maximum if γ>3 and diverges if γ<3.

Priority queues with bursty arrivals of incoming tasks

NASA Astrophysics Data System (ADS)

Masuda, N.; Kim, J. S.; Kahng, B.

2009-03-01

Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior, D(τ)˜τ-δ , where τ is the interevent time, and δ≃1 or 3/2 . The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power-law distribution Pw(τ)˜τ-α with either α=1 or 3/2 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a power-law distribution with general exponent γ . For this case, we obtain analytically the exponent α , which is not necessarily 1 or 3/2 and takes nonuniversal values depending on γ . We develop the generating function formalism to obtain the exponent α , which is distinct from the continuous time approximation used in the previous studies.

A Direct Method for Viewing Ferromagnetic Phase Transition.

ERIC Educational Resources Information Center

Lue, Chin-Shan

1994-01-01

Provides a method, using the Rowland ring as a specimen, to observe the phase transition process directly on the oscilloscope and even extract the critical exponent of ferromagnetic transition. Includes theory, experimental setup, and results. (MVL)

Critical reflexivity in financial markets: a Hawkes process analysis

NASA Astrophysics Data System (ADS)

Hardiman, Stephen J.; Bercot, Nicolas; Bouchaud, Jean-Philippe

2013-10-01

We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short times, less than ≈ 103 s, and crosses over to a second power-law regime with a larger decay exponent ≈-1.45 for longer times scales in the range [ 103,106 ] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.

Self-consistent expansion for the molecular beam epitaxy equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2002-03-01

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-->-r',t-t')=2D0\\|r-->- r'\\|2ρ-dδ(t-t'). I find a lower critical dimension dc(ρ)=4+2ρ, above which the linear MBE solution appears. Below the lower critical dimension a ρ-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.

Self-consistent expansion for the molecular beam epitaxy equation.

PubMed

Katzav, Eytan

2002-03-01

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-r('),t-t('))=2D(0)[r-->-r(')](2rho-d)delta(t-t(')). I find a lower critical dimension d(c)(rho)=4+2rho, above which the linear MBE solution appears. Below the lower critical dimension a rho-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

NASA Astrophysics Data System (ADS)

Zhang, L.; Tang, G.; Xun, Z.; Han, K.; Chen, H.; Hu, B.

2008-05-01

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

Power-Laws and Scaling in Finance: Empirical Evidence and Simple Models

NASA Astrophysics Data System (ADS)

Bouchaud, Jean-Philippe

We discuss several models that may explain the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to non universal exponents. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing `microscopic' (i.e. trader based) model that explains this observation is however not yet available. We discuss a rather generic mechanism for long-ranged volatility correlations based on the idea that agents constantly switch between active and inactive strategies depending on their relative performance.

Spin diffusion from an inhomogeneous quench in an integrable system.

PubMed

Ljubotina, Marko; Žnidarič, Marko; Prosen, Tomaž

2017-07-13

Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Bo; Zhu, Wei; Shi, Qinwei

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behaviormore » is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. Furthermore, we show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.« less

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model

NASA Astrophysics Data System (ADS)

Sousa, J. Ricardo de

A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.

Measurement of Creep Properties of Ultra-High-Temperature Materials by a Novel Non-Contact Technique

NASA Technical Reports Server (NTRS)

Hyers, Robert W.; Lee, Jonghyun; Rogers, Jan R.; Liaw, Peter K.

2007-01-01

A non-contact technique for measuring the creep properties of materials has been developed and validated as part of a collaboration among the University of Massachusetts, NASA Marshall Space Flight Center Electrostatic Levitation Facility (ESL), and the University of Tennessee. This novel method has several advantages over conventional creep testing. The sample is deformed by the centripetal acceleration from the rapid rotation, and the deformed shapes are analyzed to determine the strain. Since there is no contact with grips, there is no theoretical maximum temperature and no concern about chemical compatibility. Materials may be tested at the service temperature even for extreme environments such as rocket nozzles, or above the service temperature for accelerated testing of materials for applications such as jet engines or turbopumps for liquid-fueled engines. The creep measurements have been demonstrated to 2400 C with niobium, while the test facility, the NASA MSFC ESL, has processed materials up to 3400 C. Furthermore, the ESL creep method employs a distribution of stress to determine the stress exponent from a single test, versus the many tests required by conventional methods. Determination of the stress exponent from the ESL creep tests requires very precise measurement of the surface shape of the deformed sample for comparison to deformations predicted by finite element models for different stress exponents. An error analysis shows that the stress exponent can be determined to about 1% accuracy with the current methods and apparatus. The creep properties of single-crystal niobium at 1985 C showed excellent agreement with conventional tests performed according to ASTM Standard E-139. Tests on other metals, ceramics, and composites relevant to rocket propulsion and turbine engines are underway.

Fractality of eroded coastlines of correlated landscapes.

PubMed

Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

2011-07-01

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

Self-Organized Criticality in an Anisotropic Earthquake Model

NASA Astrophysics Data System (ADS)

Li, Bin-Quan; Wang, Sheng-Jun

2018-03-01

We have made an extensive numerical study of a modified model proposed by Olami, Feder, and Christensen to describe earthquake behavior. Two situations were considered in this paper. One situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly not averagely and keeps itself to zero. The other situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly and keeps some energy for itself instead of reset to zero. Different boundary conditions were considered as well. By analyzing the distribution of earthquake sizes, we found that self-organized criticality can be excited only in the conservative case or the approximate conservative case in the above situations. Some evidence indicated that the critical exponent of both above situations and the original OFC model tend to the same result in the conservative case. The only difference is that the avalanche size in the original model is bigger. This result may be closer to the real world, after all, every crust plate size is different. Supported by National Natural Science Foundation of China under Grant Nos. 11675096 and 11305098, the Fundamental Research Funds for the Central Universities under Grant No. GK201702001, FPALAB-SNNU under Grant No. 16QNGG007, and Interdisciplinary Incubation Project of SNU under Grant No. 5

Critical behavior in the vicinity of nematic to smectic A (N-SmA) phase transition of two polar-polar binary liquid crystalline systems

NASA Astrophysics Data System (ADS)

Barman, Barnali; Sarkar, Sudipta Kumar; Das, Malay Kumar

2018-01-01

Phase diagram, critical behavior and order of the nematic (N)-smectic A (SmA) phase transition of two polar-polar binary systems (i) 4-n-heptyloxy-4‧-cyanobiphenyl (7OCB) and 4-n-octyloxy-4‧-cyanobiphenyl (8OCB); (ii) 4-n-octyloxy-4‧-cyanobiphenyl (8OCB) and 4-n-nonyloxy-4‧-cyanobiphenyl (9OCB) by means of a high-resolution temperature scanning measurement of birefringence have been reported in this work. A simple power law analysis has been adopted to extract the specific heat critical exponent (α‧) at N-SmA transition from birefringence data. The α‧ for N-SmA transition indicates a uniform crossover behavior and has appeared to be non-universal in nature. With increasing concentration of the higher homologues for both the binary systems, the N-SmA transition reveals a strong tendency to be driven towards the tricritical nature. The 3D-XY limit (i.e. α‧ = -0.007) for N-SmA transition reaches at the concentration x8OCB = 0.28 corresponding to the McMillan ratio 0.914, whereas the tricritical point has been found to appear near x9OCB = 1.0 corresponding to McMillan ratio 0.992.

Species survival and scaling laws in hostile and disordered environments

NASA Astrophysics Data System (ADS)

Rocha, Rodrigo P.; Figueiredo, Wagner; Suweis, Samir; Maritan, Amos

2016-10-01

In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival. We perform a finite-size scaling and we obtain the associated scaling exponents. In addition, we show that the PDF of the critical patch sizes has an universal shape for the 1D case in terms of the model parameters (diffusion, growth rate, etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF of the critical patch sizes of the fractal Peano basin, and it does not obey the same scaling law of the 1D case.

Onset of meso-scale turbulence in active nematics

NASA Astrophysics Data System (ADS)

Doostmohammadi, Amin; Shendruk, Tyler N.; Thijssen, Kristian; Yeomans, Julia M.

2017-05-01

Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at low Reynolds number in fluidized biological systems. This spatiotemporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here we show how the motion of active matter along a micro-channel transitions to meso-scale turbulence through the evolution of locally disordered patches (active puffs) from an ordered vortex-lattice flow state. We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in a channel coincide with the directed percolation universality class. This finding bridges our understanding of the onset of low-Reynolds-number meso-scale turbulence and traditional scale-invariant turbulence in confinement.

Mutual information, neural networks and the renormalization group

NASA Astrophysics Data System (ADS)

Koch-Janusz, Maciej; Ringel, Zohar

2018-06-01

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

Multiplicity of solutions of the bi-harmonic Schrödinger equation with critical growth

NASA Astrophysics Data System (ADS)

Zhang, Jian; Lou, Zhenluo; Ji, Yanju; Shao, Wei

2018-04-01

In this paper, we study multiplicity of solutions of the critical bi-harmonic equation ɛ ^4 Δ ^2 u +V(x) u =h(x) f(u)+g(x) u^{2_*-1} in R^N, where 2_*=2N/N-4 is the critical exponent. When ɛ >0 is small, we establish the relationship between the number of solutions and the profile of V, h, g. Also, without the restriction on ɛ , we obtain a multiplicity result.

Competition-Induced Criticality in a Model of Meme Popularity

NASA Astrophysics Data System (ADS)

Gleeson, James P.; Ward, Jonathan A.; O'Sullivan, Kevin P.; Lee, William T.

2014-01-01

Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent α <2, unlike preferential-attachment models), similar to those seen in empirical data.

Competition-induced criticality in a model of meme popularity.

PubMed

Gleeson, James P; Ward, Jonathan A; O'Sullivan, Kevin P; Lee, William T

2014-01-31

Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent α<2, unlike preferential-attachment models), similar to those seen in empirical data.

Las Matematicas: Lenguaje Universal. Nivel 1: Numeros y Numeracion (Mathematics: A Universal Language. Level 1: Numbers and Numeration).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include graphing on a number line, place value, using exponents, flow charts, and Roman numerals. (MK)

DNA bubble dynamics as a quantum Coulomb problem.

PubMed

Fogedby, Hans C; Metzler, Ralf

2007-02-16

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution W(t). Below Tm, W(t) is associated with the continuum of scattering states of the repulsive Coulomb potential. At Tm, the Coulomb potential vanishes and W(t) assumes a power-law tail with nontrivial dynamic exponents: the critical exponent of the entropy loss factor may cause a finite mean lifetime. Above Tm (attractive potential), the long-time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Effects of film growth kinetics on grain coarsening and grain shape.

PubMed

Reis, F D A Aarão

2017-04-01

We study models of grain nucleation and coarsening during the deposition of a thin film using numerical simulations and scaling approaches. The incorporation of new particles in the film is determined by lattice growth models in three different universality classes, with no effect of the grain structure. The first model of grain coarsening is similar to that proposed by Saito and Omura [Phys. Rev. E 84, 021601 (2011)PLEEE81539-375510.1103/PhysRevE.84.021601], in which nucleation occurs only at the substrate, and the grain boundary evolution at the film surface is determined by a probabilistic competition of neighboring grains. The surface grain density has a power-law decay, with an exponent related to the dynamical exponent of the underlying growth kinetics, and the average radius of gyration scales with the film thickness with the same exponent. This model is extended by allowing nucleation of new grains during the deposition, with constant but small rates. The surface grain density crosses over from the initial power law decay to a saturation; at the crossover, the time, grain mass, and surface grain density are estimated as a function of the nucleation rate. The distributions of grain mass, height, and radius of gyration show remarkable power law decays, similar to other systems with coarsening and particle injection, with exponents also related to the dynamical exponent. The scaling of the radius of gyration with the height h relative to the base of the grain show clearly different exponents in growth dominated by surface tension and growth dominated by surface diffusion; thus it may be interesting for investigating the effects of kinetic roughening on grain morphology. In growth dominated by surface diffusion, the increase of grain size with temperature is observed.

How big, and how long-lasting, will an extreme burst above threshold be ? Lessons from self-organised criticality

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chapman, S. C.; Hnat, B.

2011-12-01

The idea that there might not be a typical scale for energy release in some space physics systems is a relatively new one [see e.g. mini-review of early work in Freeman and Watkins, Science, 2002; & Aschwanden, Self Organized Criticality (SOC) in Astrophysics, Springer, 2011]. In part it resulted from the widespread approximate fractality seen elsewhere in nature. SOC was introduced by Bak et al [PRL, 1987] as a physical explanation of such widespread space-time fractality. SOC inspired the introduction into magnetospheric physics of "burst" diagnostics by Takalo [1993] & Consolini [1996]. These quantified events in a time series by "size" (integrated area above a fixed threshold) and "duration", and revealed a long tailed population of events across a broad range of sizes, subsequently also seen in solar wind drivers like Akasofu's epsilon function [Freeman et al, PRE & GRL, 2000]. Spatiotemporal bursts have an interest beyond SOC, however. Estimating the probability of a burst of a given size and duration bears directly on the problem of correlated extreme events, or "bunched black swans" [e.g. Watkins et al, EGU, 2011 presentation at the URL below]. With a view both to space physics and this wider context we here consider an interesting development of the burst idea made by Uritsky et al [GRL, 2001]. These authors adapted the spatiotemporal spreading exponent [e.g. Marro & Dickman, Nonequilibrium phase transitions in lattice models, 1999], calculating a superposed epoch average of surviving activity in bursts after their first excursion above a threshold. In a 1D time series, the 1-minute AL auroral index (averaged over 5 minutes), they found scaling behaviour up to ~ 2 hours. We investigate the relationships between exponents found by this method and other, more widely known exponents governing a fractal (or multifractal) time series such as the self-similarity exponent H and long-range dependence exponent d. We conclude by discussing the applications of these techniques to problems such as the forecasting the probability of a single short-lived large burst versus that of a long correlated sequence of more moderate exceedences above a threshold.

Effect of hockey-stick-shaped molecules on the critical behavior at the nematic to isotropic and smectic-A to nematic phase transitions in octylcyanobiphenyl

NASA Astrophysics Data System (ADS)

Chakraborty, Anish; Chakraborty, Susanta; Das, Malay Kumar

2015-03-01

In the field of soft matter research, the characteristic behavior of both nematic-isotropic (N -I ) and smectic-A nematic (Sm -A N ) phase transitions has gained considerable attention due to their several attractive features. In this work, a high-resolution measurement of optical birefringence (Δ n ) has been performed to probe the critical behavior at the N -I and Sm -A N phase transitions in a binary system comprising the rodlike octylcyanobiphenyl and a laterally methyl substituted hockey-stick-shaped mesogen, 4-(3-n -decyloxy-2-methyl-phenyliminomethyl)phenyl 4-n -dodecyloxycinnamate. For the investigated mixtures, the critical exponent β related to the limiting behavior of the nematic order parameter close to the N -I phase transition has come out to be in good conformity with the tricritical hypothesis. Moreover, the yielded effective critical exponents (α', β', γ') characterizing the critical fluctuation near the Sm -A N phase transition have appeared to be nonuniversal in nature. With increasing hockey-stick-shaped dopant concentration, the Sm -A N phase transition demonstrates a strong tendency to be driven towards a first-order nature. Such a behavior has been accounted for by considering a modification of the effective intermolecular interactions and hence the related coupling between the nematic and smectic order parameters, caused by the introduction of the angular mesogenic molecules.

Intermittency and universality of small scales of passive scalar in turbulence

NASA Astrophysics Data System (ADS)

Gotoh, Toshiyuki; Watanabe, Takeshi

2014-11-01

Recent experiments and Direct Numerical Simulations (DNSs) suggest that the small scale statistics of passive scalar may not be as ``universal'' as in the velocity case. To address this problem, we study the moments of scalar increment in steady turbulence at Rλ > 800 by using DNS up to the grid points of 40963. In order for the scalar and turbulent flow to be as faithful as possible to the assumptions that would be made in theories, Scalar 1 and Scalar 2 are simultaneously convected by the identical isotropic turbulent flow but excited by two different methods. Scalar 1 is excited by the random scalar injection which is isotropic, Gaussian and white in time at low wavenumber band, while Scalar 2 is excited by the uniform mean scalar gradient. The moments of two scalars as functions of the separation vector are expanded in terms of the Legendre polynomials to extract the scaling exponents of the moments up to the 4th anisotropic sector for Scalar 2. It is found that the exponents of the isotropic sectors seem to have the same values at separation distances in the narrow range over which the 4/3 law holds simultaneously for two scalars. The exponents of the anisotropic sectors and the cumulants of the moments will also be reported. HPCI, JHPCN, Grant-in-Aid for Sci. Res. No.24360068, Ministry of Edu. Sci., Japan.

Centrifuge impact cratering experiments: Scaling laws for non-porous targets

NASA Technical Reports Server (NTRS)

Schmidt, Robert M.

1987-01-01

A geotechnical centrifuge was used to investigate large body impacts onto planetary surfaces. At elevated gravity, it is possible to match various dimensionless similarity parameters which were shown to govern large scale impacts. Observations of crater growth and target flow fields have provided detailed and critical tests of a complete and unified scaling theory for impact cratering. Scaling estimates were determined for nonporous targets. Scaling estimates for large scale cratering in rock proposed previously by others have assumed that the crater radius is proportional to powers of the impactor energy and gravity, with no additional dependence on impact velocity. The size scaling laws determined from ongoing centrifuge experiments differ from earlier ones in three respects. First, a distinct dependence of impact velocity is recognized, even for constant impactor energy. Second, the present energy exponent for low porosity targets, like competent rock, is lower than earlier estimates. Third, the gravity exponent is recognized here as being related to both the energy and the velocity exponents.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

Bipartite fidelity and Loschmidt echo of the bosonic conformal interface

NASA Astrophysics Data System (ADS)

Zhou, Tianci; Lin, Mao

2017-12-01

We study the quantum quench problem for a class of bosonic conformal interfaces by computing the Loschmidt echo and the bipartite fidelity. The quench can be viewed as a sudden change of boundary conditions parametrized by θ when connecting two one-dimensional critical systems. They are classified by S (θ ) matrices associated with the current scattering processes on the interface. The resulting Loschmidt echo of the quench has long time algebraic decay t-α, whose exponent also appears in the finite size bipartite fidelity as L-α/2. We perform analytic and numerical calculations of the exponent α , and find that it has a quadratic dependence on the change of θ if the prior and post-quench boundary conditions are of the same type of S , while remaining 1/4 otherwise. Possible physical realizations of these interfaces include, for instance, connecting different quantum wires (Luttinger liquids), quench of the topological phase edge states, etc., and the exponent can be detected in an x-ray edge singularity-type experiment.

Critical desertification transition in semi-arid ecosystems: The role of local facilitation and colonization rate

NASA Astrophysics Data System (ADS)

Corrado, Raffaele; Cherubini, Anna Maria; Pennetta, Cecilia

2015-05-01

In this work we study the effect of two different ecological mechanisms on the desertification transition in arid or semi-arid ecosystems, modeled by a stochastic cellular automaton. Namely we consider the role of the facilitation mechanism, i.e. the local positive effects of plants on their neighborhood and of colonization factors, such as seed production, survival and germination probabilities. Within the model, the strength of these two mechanisms is determined by the parameters f and b, respectively controlling the rates of the recovery and colonization processes. In particular we focus on the full desertification transition occurring at increasing value of the mortality rate m and we discuss how the values of f and b affect the critical mortality mc , the critical exponents β and γσ‧, determining the power-law scaling of the average vegetation density and of the root-mean-square deviation of the density fluctuations, and the character of the transition: continuous or abrupt. We show that mc strongly depends on both f and b, a dependence which accounts for the higher resilience of the ecosystems to external stresses as a consequence of an increased effectiveness of positive feedback effects. On the other hand, concerning the value of the exponents and the character of the transition, our results point out that both these features are unaffected by changes in the strength of the local facilitation. Viceversa, we show that an increase of the colonization factor b significantly modifies the values of the exponents and the order of the transition, changing a continuous transition into an abrupt one. We explain these results in terms of the different range of the interactions characterizing facilitation and colonization mechanisms.

Spatio-temporal correlations in the Manna model in one, three and five dimensions

NASA Astrophysics Data System (ADS)

Willis, Gary; Pruessner, Gunnar

2018-02-01

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

Quantum criticality of a spin-1 XY model with easy-plane single-ion anisotropy via a two-time Green function approach avoiding the Anderson-Callen decoupling

NASA Astrophysics Data System (ADS)

Mercaldo, M. T.; Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.

2016-04-01

In this work we study the quantum phase transition, the phase diagram and the quantum criticality induced by the easy-plane single-ion anisotropy in a d-dimensional quantum spin-1 XY model in absence of an external longitudinal magnetic field. We employ the two-time Green function method by avoiding the Anderson-Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. Remarkably, the equivalence between the microscopic spin model and the continuous O(2) -vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. The zero-temperature critic anisotropy parameter Dc is obtained for dimensionalities d > 1 as a function of the microscopic exchange coupling parameter and the related numerical data for different lattices are found to be in reasonable agreement with those obtained by means of alternative analytical and numerical methods. For d > 2, and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. The main crossover lines between different asymptotic regimes around the quantum critical point are also estimated providing a global phase diagram and a quantum criticality very similar to the conventional ones.

Finite-Size Scaling Analysis of Binary Stochastic Processes and Universality Classes of Information Cascade Phase Transition

NASA Astrophysics Data System (ADS)

Mori, Shintaro; Hisakado, Masato

2015-05-01

We propose a finite-size scaling analysis method for binary stochastic processes X(t) in { 0,1} based on the second moment correlation length ξ for the autocorrelation function C(t). The purpose is to clarify the critical properties and provide a new data analysis method for information cascades. As a simple model to represent the different behaviors of subjects in information cascade experiments, we assume that X(t) is a mixture of an independent random variable that takes 1 with probability q and a random variable that depends on the ratio z of the variables taking 1 among recent r variables. We consider two types of the probability f(z) that the latter takes 1: (i) analog [f(z) = z] and (ii) digital [f(z) = θ(z - 1/2)]. We study the universal functions of scaling for ξ and the integrated correlation time τ. For finite r, C(t) decays exponentially as a function of t, and there is only one stable renormalization group (RG) fixed point. In the limit r to ∞ , where X(t) depends on all the previous variables, C(t) in model (i) obeys a power law, and the system becomes scale invariant. In model (ii) with q ≠ 1/2, there are two stable RG fixed points, which correspond to the ordered and disordered phases of the information cascade phase transition with the critical exponents β = 1 and ν|| = 2.

Scaling exponents for ordered maxima

DOE PAGES

Ben-Naim, E.; Krapivsky, P. L.; Lemons, N. W.

2015-12-22

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S N that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S N is universal: it does not depend on themore » distribution from which the random variables are drawn. For two sequences, S N~N –1/2, and in general, the decay is algebraic, S N~N –σm, for large N. We analytically obtain the exponent σ 3≅1.302931 as root of a transcendental equation. Moreover, the exponents σ m grow with m, and we show that σ m~m for large m.« less

Inhomogeneous distribution of water droplets in cloud turbulence

NASA Astrophysics Data System (ADS)

Fouxon, Itzhak; Park, Yongnam; Harduf, Roei; Lee, Changhoon

2015-09-01

We consider sedimentation of small particles in the turbulent flow where fluid accelerations are much smaller than acceleration of gravity g . The particles are dragged by the flow by linear friction force. We demonstrate that the pair-correlation function of particles' concentration diverges with decreasing separation as a power law with negative exponent. This manifests fractal distribution of particles in space. We find that the exponent is proportional to ratio of integral of energy spectrum of turbulence times the wave number over g . The proportionality coefficient is a universal number independent of particle size. We derive the spectrum of Lyapunov exponents that describes the evolution of small patches of particles. It is demonstrated that particles separate dominantly in the horizontal plane. This provides a theory for the recently observed vertical columns formed by the particles. We confirm the predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include conditions that hold for water droplets in warm clouds thus providing a tool for the prediction of rain formation.

Nonuniversality of the Archie exponent due to multifractality of resistivity well logs

NASA Astrophysics Data System (ADS)

Dashtian, Hassan; Yang, Yafan; Sahimi, Muhammad

2015-12-01

Archie's law expresses a relation between the formation factor F of porous media and their porosity ϕ, F∝ϕ-m, where m is the Archie or the cementation exponent. Despite widespread use of Archie's law, the value of m and whether it is universal and independent of the type of reservoir have remained controversial. We analyze various porosity and resistivity logs along 36 wells in six Iranian oil and gas reservoirs using wavelet transform coherence and multifractal detrended fluctuation analysis. m is estimated for two sets of data: one set contains the resistivity data that include those segments of the well that contain significant clay content and one without. The analysis indicates that the well logs are multifractal and that due to the multifractality the exponent m is nonuniversal. Thus, analysis of the resistivity of laboratory or outcrop samples that are not multifractal yields estimates of m that are not applicable to well logs in oil or gas reservoirs.

Application of computational statistical physics to scale invariance and universality in economic phenomena

NASA Astrophysics Data System (ADS)

Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.

2002-06-01

This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly-discovered scaling results that appear to be "universal", in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function (PDF), which is a simple power law with exponent -4 extending over 10 2 standard deviations (a factor of 10 8 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious "symmetry breaking" for values of Σ above a certain threshold value Σc; here Σ is defined to be the local first moment of the probability distribution of demand Ω—the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature.

On the Plasticity of Amorphous Solids

NASA Astrophysics Data System (ADS)

Lin, Jie

Mechanical behaviors of amorphous materials under external stress are central to various phenomena including earthquakes and landslides. Most amorphous materials possess a well defined yield stress when thermal fluctuations are negligible. Only when the shear stress is above the yield stress, the material can flow as a fluid, otherwise it deforms as a solid. There are accumulating evidences that the yielding transition between the flowing and solid phase is a critical phenomenon, and one evidence is the long ranged correlations of plastic strain during adiabatic shear. In spite of this, we still have not fully understood the associated critical exponents and their scaling relations. In the last decade, it has been widely accepted that the elementary rearrangements in amorphous solids are not well-defined topological defects as crystals, instead they are local irreversible rearrangements of a few particles, denoted as shear transformations. Because a single shear transformation changes the local arrangement of particles, it therefore generates an elastic stress field propagating over the whole system. The resulting changes in the local stresses in other regions of the system may in turn trigger more shear transformations. A central feature that complicates the yielding transition is the long range and anisotropic stress field generated by shear transformations. This peculiar interaction between shear transformations leads to two important characteristics: 1.the mechanical noises generated by plastic deformation are broadly distributed 2.those regions that are undergoing plastic deformation has equal probability to make other parts of the material to be more stable or more unstable, depending on the direction between them. In this thesis, we show that these two important factors leads to a singular density of shear transformations, P( x) xtheta at small x, where x is a local measure of stability, namely, the extra stress one needs to add locally to reach the elastic instabilities. We denote such a singular distribution as a pseudo gap, and the theta exponent as the pseudo gap exponent. The fact that the plastic avalanche rates, i.e., number of avalanches per unit strain, during quasi-static shear is not proportional to system size implies the existence of a finite pseudo gap exponent. Arguments based on stability against local perturbations lead to a lower bound of the pseudo gap exponents. In the flowing phase, we construct the scaling description of the yielding transition of soft amorphous solids at zero temperature. The yielding transition shares similarities with another well studied dynamic phase transition, the depinning transition where an elastic interface is driven in a disordered medium, however, there are also striking differences between them. Avalanches are fractal in the yielding transition, characterized by a fractal dimension smaller than the spatial dimension, while avalanches are compact with a fractal dimension, not smaller than the spatial dimension in the depinning transition. We make connections between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress, the extension and duration of the avalanches of plasticity, and the pseudo gap exponent. On the other hand, in the solid phase, the pseudo gap also plays a significant role as one increases the shear stress adiabatically. We point out the connection between the local slope of stress-strain curve in the transient state and mean avalanche sizes as the system approaches failure. We argue that the entire solid phase below the yield stress is critical as long as there is finite amount of plastic strain, and plasticity always involves system-spanning events because of the finite pseudo gap exponent. We use the elasto-plastic model, a mesoscopic approach, to verify our theoretical predictions and obtain satisfying results. Finally, a mean field description of plastic flow in amorphous solids are proposed and solved analytically. The mean field models captures the broad distribution of mechanical noise generated by plasticity, leading to a biased Levy flight behavior of local stresses, with the elastic instabilities as the absorbing boundary. The mean field model implies an upper critical dimension as dc = 4.

Special course for Masters and PhD students: phase transitions, Landau theory, 1D Ising model, the dimension of the space and Cosmology

NASA Astrophysics Data System (ADS)

Udodov, Vladimir; Katanov Khakas State Univ Team

2014-03-01

Symmetry breaking transitions. The phenomenological (L.D.Landau, USSR, 1937) way to describe phase transitions (PT's). Order parameter and loss of the symmetry. The second derivative of the free energy changes jump wise at the transition, i.e. we have a mathematical singularity and second order PT (TC>0). Extremes of free energy. A point of loss of stability of the symmetrical phase. The eigenfrequency of PT and soft mode behavior. The conditions of applicability of the Landau theory (A.Levanyuk, 1959, V.Ginzburg, 1960). 1D Ising model and exact solution by a transfer matrix method. Critical exponents in the L.Landau PT's theory and for 1D Ising model. Scaling hypothesis (1965) for 1D Ising model with zero critical temperature. The order of PT in 1D Ising model in the framework of the R.Baxter approach. The anthropic principle and the dimension of the space. Why do we have a three-dimensional space? Big bang, the cosmic vacuum, inflation and PT's. Higgs boson and symmetry breaking transitions. Author acknowledges the support of Katanov Khakas State University.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor

2016-06-01

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Percolation behavior of polymer/metal composites on modification of filler

NASA Astrophysics Data System (ADS)

Panda, M.; Srinivas, V.; Thakur, A. K.

2014-02-01

Polymer-metal composites with different fillers, such as nanocrystalline nickel (n-Ni), core shell n-Ni and nickel oxide (NiO)[n-Ni@NiO] were prepared under the same processing conditions with polyvinyledene fluoride matrix. The larger value of critical exponents (s and s') and percolation threshold (fc 0.30) for n-Ni@NiO composites as compared to n-Ni composites (fc 0.07) and a comparable effective dielectric constant (ɛeff 300) with low loss tangent (tan δ 0.1) at 100 Hz in case of percolative n-Ni@NiO composite was observed. The core shell structure [n-Ni@NiO] also shows a very high value of ɛeff 6000 with tan δ 8 at 40 Hz. The results have been explained by using boundary layer capacitor effect and the percolation theory. The difference in fc and critical exponents is attributed to NiO insulating layer that gives rise to different extent of continuumness at fc and have been explained with the help of Swiss cheese model.

Criticality and Chaos in Systems of Communities

NASA Astrophysics Data System (ADS)

Ostilli, Massimo; Figueiredo, Wagner

2016-01-01

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.

PubMed

Saichev, A; Sornette, D

2005-05-01

Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth's law. Our theory shows that Båth's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +/- 0.1 for Båth's constant value around 1.2, our exact analytical treatment of Båth's law provides new constraints on the productivity exponent alpha and the branching ratio n: 0.9 approximately < alpha < or =1. We propose a method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the "second Båth law for foreshocks:" the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude rho.

Intrinsic pinning and the critical current scaling of clean epitaxial Fe(Se,Te) thin films

NASA Astrophysics Data System (ADS)

Iida, Kazumasa; Hänisch, Jens; Reich, Elke; Kurth, Fritz; Hühne, Ruben; Schultz, Ludwig; Holzapfel, Bernhard; Ichinose, Ataru; Hanawa, Masafumi; Tsukada, Ichiro; Schulze, Michael; Aswartham, Saicharan; Wurmehl, Sabine; Büchner, Bernd

2013-03-01

We report on the transport properties of clean, epitaxial Fe(Se,Te) thin films prepared on Fe-buffered MgO (001) single crystalline substrates by pulsed laser deposition. Near Tc a steep slope of the upper critical field for H||ab was observed (74.1 T/K), leading to a very short out-of-plane coherence length, ξc(0), of 0.2 nm, yielding 2ξc(0)≈0.4nm. This value is shorter than the interlayer distance (0.605 nm) between the Fe-Se(Te) planes, indicative of modulation of the superconducting order parameter along the c axis. An inverse correlation between the power law exponent N of the electric field-current density(E-J) curve and the critical current density Jc has been observed at 4 K, when the orientation of H was close to the ab plane. These results prove the presence of intrinsic pinning in Fe(Se,Te). A successful scaling of the angular dependent Jc and the corresponding exponent N can be realized by the anisotropic Ginzburg Landau approach with appropriate Γ values 2˜3.5. The temperature dependence of Γ behaves almost identically to that of the penetration depth anisotropy.

Critical behavior study around the ferromagnetic phase transition in Pr2Pt2In

NASA Astrophysics Data System (ADS)

Tchokonté, M. B. Tchoula; Mboukam, J. J.; Sondezi, B. M.; Bashir, A. K. H.; Britz, D.; Strydom, A. M.; Kaczorowski, D.

2018-05-01

The magnetic ordering in Pr2Pt2In was investigated by means of magnetization and magnetic susceptibility measurements. The compound was found to order ferromagnetically at TC = 8.8(2) K with a second-order phase transition. The derived critical exponents β = 0.325(2), γ = 1.058(2) and δ = 4.26(4) are close to those expected for a 3D Ising ferromagnet.

Exact renormalization group equation for the Lifshitz critical point

NASA Astrophysics Data System (ADS)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Shock-wave flow regimes at entry into the diffuser of a hypersonic ramjet engine: Influence of physical properties of the gas medium

NASA Astrophysics Data System (ADS)

Tarnavskii, G. A.

2006-07-01

The physical aspects of the effective-adiabatic-exponent model making it possible to decompose the total problem on modeling of high-velocity gas flows into individual subproblems (“physicochemical processes” and “ aeromechanics”), which ensures the creation of a universal and efficient computer complex divided into a number of independent units, have been analyzed. Shock-wave structures appearing at entry into the duct of a hypersonic aircraft have been investigated based on this methodology, and the influence of the physical properties of the gas medium in a wide range of variations of the effective adiabatic exponent has been studied.

Allometric scaling of strength scores in NCAA division I-A football athletes.

PubMed

Oba, Yukiya; Hetzler, Ronald K; Stickley, Christopher D; Tamura, Kaori; Kimura, Iris F; Heffernan, Thomas P

2014-12-01

This study examined population-specific allometric exponents to control for the effect of body mass (BM) on bench press, clean, and squat strength measures among Division I-A collegiate football athletes. One repetition maximum data were obtained from a university pre-season football strength assessment (bench press, n = 207; clean, n = 88; and squat n = 86) and categorized into 3 groups by positions (line, linebacker, and skill). Regression diagnostics and correlations of scaled strength data to BM were used to assess the efficacy of the allometric scaling model and contrasted with that of ratio scaling and theoretically based allometric exponents of 0.67 and 0.33. The log-linear regression models yielded the following exponents (b): b = 0.559, 0.287, and 0.496 for bench press, clean, and squat, respectively. Correlations between bench press, clean, and squat to BM were r = -0.024, -0.047, and -0.018, respectively, suggesting that the derived allometric exponents were effective in partialling out the effect of BM on these lifts and removing between-group differences. Conversely, unscaled, ratio-scaled, and allometrically scaled (b = 0.67 or 0.33) data resulted in significant differences between groups. It is suggested that the exponents derived in the present study be used for allometrically scaling strength measures in National Collegiate Athletic Association Division I-A football athletes. Use of the normative percentile rank scores provide coaches and trainers with a valid means of judging the effectiveness of their training programs by allowing comparisons between individuals without the confounding influence of BM.

Critical behavior of dissipative two-dimensional spin lattices

NASA Astrophysics Data System (ADS)

Rota, R.; Storme, F.; Bartolo, N.; Fazio, R.; Ciuti, C.

2017-04-01

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian that are subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated with a dissipative ferromagnetic transition. We show that the von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information, which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition.

Criticality and turbulence in a resistive magnetohydrodynamic current sheet

NASA Astrophysics Data System (ADS)

Klimas, Alexander J.; Uritsky, Vadim M.

2017-02-01

Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks.

PubMed

Lombardi, F; Herrmann, H J; de Arcangelis, L

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks

NASA Astrophysics Data System (ADS)

Lombardi, F.; Herrmann, H. J.; de Arcangelis, L.

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

Criticality and turbulence in a resistive magnetohydrodynamic current sheet.

PubMed

Klimas, Alexander J; Uritsky, Vadim M

2017-02-01

Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.

Ising kinetics with hundred Giga-sites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stauffer, D.; Knecht, R.

1996-12-01

From presumed world-record simulations up to 4800{sup 3} and 112{sup 5} and from the Ito algorithm applied to smaller 3D lattices we obtain the dynamical critical exponent z near 2.05 in three dimensions and J/{kappa}{sub B}T{sub c} = 0.11391 in five.

Self-organized criticality in a cold plasma

NASA Astrophysics Data System (ADS)

Alex, Prince; Carreras, Benjamin Andres; Arumugam, Saravanan; Sinha, Suraj Kumar

2017-12-01

We present direct evidence for the existence of self-organized critical behavior in cold plasma. A multiple anodic double layer structure generated in a double discharge plasma setup shows critical behavior for the anode bias above a threshold value. Analysis of the floating potential fluctuations reveals the existence of long-range time correlations and power law behavior in the tail of the probability distribution function of the fluctuations. The measured Hurst exponent and the power law tail in the rank function are strong indication of the self-organized critical behavior of the system and hence provide a condition under which complexities arise in cold plasma.

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana.

PubMed

Vasseur, François; Exposito-Alonso, Moises; Ayala-Garay, Oscar J; Wang, George; Enquist, Brian J; Vile, Denis; Violle, Cyrille; Weigel, Detlef

2018-03-27

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4 , has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes. Copyright © 2018 the Author(s). Published by PNAS.

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana

PubMed Central

Vasseur, François; Ayala-Garay, Oscar J.; Wang, George; Enquist, Brian J.; Vile, Denis; Violle, Cyrille

2018-01-01

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes. PMID:29540570

Universality of modulation length and time exponents.

PubMed

Chakrabarty, Saurish; Dobrosavljević, Vladimir; Seidel, Alexander; Nussinov, Zohar

2012-10-01

We study systems with a crossover parameter λ, such as the temperature T, which has a threshold value λ(*) across which the correlation function changes from exhibiting fixed wavelength (or time period) modulations to continuously varying modulation lengths (or times). We introduce a hitherto unknown exponent ν(L) characterizing the universal nature of this crossover and compute its value in general instances. This exponent, similar to standard correlation length exponents, is obtained from motion of the poles of the momentum (or frequency) space correlation functions in the complex k-plane (or ω-plane) as the parameter λ is varied. Near the crossover (i.e., for λ→λ(*)), the characteristic modulation wave vector K(R) in the variable modulation length "phase" is related to that in the fixed modulation length "phase" q via |K(R)-q|[proportionality]|T-T(*)|(νL). We find, in general, that ν(L)=1/2. In some special instances, ν(L) may attain other rational values. We extend this result to general problems in which the eigenvalue of an operator or a pole characterizing general response functions may attain a constant real (or imaginary) part beyond a particular threshold value λ(*). We discuss extensions of this result to multiple other arenas. These include the axial next-nearest-neighbor Ising (ANNNI) model. By extending our considerations, we comment on relations pertaining not only to the modulation lengths (or times), but also to the standard correlation lengths (or times). We introduce the notion of a Josephson time scale. We comment on the presence of aperiodic "chaotic" modulations in "soft-spin" and other systems. These relate to glass-type features. We discuss applications to Fermi systems, with particular application to metal to band insulator transitions, change of Fermi surface topology, divergent effective masses, Dirac systems, and topological insulators. Both regular periodic and glassy (and spatially chaotic behavior) may be found in strongly correlated electronic systems.

Universal scaling function in discrete time asymmetric exclusion processes

NASA Astrophysics Data System (ADS)

Chia, Nicholas; Bundschuh, Ralf

2005-03-01

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz' original publication this universality has been verified for a variety of continuous time systems in the KPZ universality class. We study the Derrida-Lebowitz scaling function for multi-particle versions of the discrete time Asymmetric Exclusion Process. We find that in this discrete time system the Derrida-Lebowitz scaling function not only properly characterizes the large system size limit, but even accurately describes surprisingly small systems. These results have immediate applications in searching biological sequence databases.

In modelling effects of global warming, invalid assumptions lead to unrealistic projections.

PubMed

Lefevre, Sjannie; McKenzie, David J; Nilsson, Göran E

2018-02-01

In their recent Opinion, Pauly and Cheung () provide new projections of future maximum fish weight (W ∞ ). Based on criticism by Lefevre et al. (2017) they changed the scaling exponent for anabolism, d G . Here we find that changing both d G and the scaling exponent for catabolism, b, leads to the projection that fish may even become 98% smaller with a 1°C increase in temperature. This unrealistic outcome indicates that the current W ∞ is unlikely to be explained by the Gill-Oxygen Limitation Theory (GOLT) and, therefore, GOLT cannot be used as a mechanistic basis for model projections about fish size in a warmer world. © 2017 John Wiley & Sons Ltd.

Benford's law gives better scaling exponents in phase transitions of quantum XY models.

PubMed

Rane, Ameya Deepak; Mishra, Utkarsh; Biswas, Anindya; Sen De, Aditi; Sen, Ujjwal

2014-08-01

Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.

On electromechanical instability in semicrystalline polymer

NASA Astrophysics Data System (ADS)

Yong, Huadong; Zhou, Youhe

2013-10-01

Semicrystalline polymers are promising materials for actuators and capacitors. In response to the electric field, the polymer undergoes large deformation. Based on a simple model, the critical electric field in the polymer is investigated in the present paper. The polymer is assumed to be incompressible and specified by the power law relation. Using the stability condition of the determinant of the Hessian, the critical electric field can be obtained. Comparing the results from prestress with prestrain, it is shown that the critical electric field is related to the hardening exponent N and may be restricted by the necking instability.

92 Years of the Ising Model: A High Resolution Monte Carlo Study

NASA Astrophysics Data System (ADS)

Xu, Jiahao; Ferrenberg, Alan M.; Landau, David P.

2018-04-01

Using extensive Monte Carlo simulations that employ the Wolff cluster flipping and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising model with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, we obtained the critical inverse temperature K c = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86) with precision that improves upon previous Monte Carlo estimates.

Cosmological evolution of generalized non-local gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xue; Wu, Ya-Bo; Liu, Yu-Chen

2016-07-01

We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term m {sup 2} {sup n} {sup -2} R □{sup -} {sup n} R to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent n . We find that the half of the scalar fields are always ghost-like and the exponent n must be taken even number for amore » stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent n should be even numbers by the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of n =2.« less

Multiple Quantum Phase Transitions in a two-dimensional superconductor

NASA Astrophysics Data System (ADS)

Bergeal, Nicolas; Biscaras, J.; Hurand, S.; Feuillet-Palma, C.; Lesueur, J.; Budhani, R. C.; Rastogi, A.; Caprara, S.; Grilli, M.

2013-03-01

We studied the magnetic field driven Quantum Phase Transition (QPT) in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through finite size scaling analysis, we showed that it belongs to the (2 +1)D XY model universality class. The system can be described as a disordered array of superconducting islands coupled by a two dimensional electron gas (2DEG). Depending on the 2DEG conductance tuned by the gate voltage, the QPT is single (corresponding to the long range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). By retrieving the coherence length critical exponent ν, we showed that the QPT can be ``clean'' or ``dirty'' according to the Harris criteria, depending on whether the phase coherence length is smaller or larger than the island size. The overall behaviour is well described by a model of coupled superconducting puddles in the framework of the fermionic scenario of 2D superconducting QPT.

Fulde-Ferrell-Larkin-Ovchinnikov correlation and free fluids in the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

In this Rapid Communication, we show that low-energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low-temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially polarized phase. We then show that for such an FFLO-like state in the low-density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility, and specific heat obey simple additivity rules, indicating the "free" particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility, which provide universal macroscopic properties and dimensionless constants of interacting fermions at low energy.

Numerical study of Potts models with aperiodic modulations: influence on first-order transitions

NASA Astrophysics Data System (ADS)

Branco, Nilton; Girardi, Daniel

2012-02-01

We perform a numerical study of Potts models on a rectangular lattice with aperiodic interactions along one spatial direction. The number of states q is such that the transition is a first-order one for the uniform model. The Wolff algorithm is employed, for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, such that the exact critical temperature is known: this leads to precise results for the exponents. We analyze models with q=6 and 15 and show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. The new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

NASA Astrophysics Data System (ADS)

Pixley, J. H.; Cole, William S.; Spielman, I. B.; Rizzi, Matteo; Das Sarma, S.

2017-10-01

We study the odd-integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a universality class with critical exponents associated with the divergence of the correlation length ν ≈2 /3 and the order-parameter susceptibility γ ≈1 /2 . We solve the effective spin model exactly using the density-matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

Enhancement of high dielectric permittivity in CaCu3Ti4O12/RuO2 composites in the vicinity of the percolation threshold

NASA Astrophysics Data System (ADS)

Mukherjee, Rupam; Lawes, Gavin; Nadgorny, Boris

2014-08-01

We observe the large enhancement in the dielectric permittivity near the percolation threshold in a composite nanoparticle system consisting of metallic RuO2 grains embedded into CaCu3Ti4O12 (CCTO) matrix and annealed at 1100 °C. To understand the nature of the dielectric response, we prepared CCTO by using standard solid state and sol-gel processes, with the relative permittivity found to be on the order of 103-104 at 10 kHz. For RuO2/CCTO composites, an increase in the real part of the dielectric permittivity by approximately an order of magnitude is observed in the vicinity of the percolation threshold, with moderate losses at room temperature. The critical exponent of dielectric permittivity and conductivity of these composites are lower than universal value (0.8-1). In these composite systems, both Maxwell-Wagner and percolation effects have been found responsible for the enhancement of dielectric permittivity.

A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

NASA Astrophysics Data System (ADS)

Gandica, Y.; Medina, E.; Bonalde, I.

2013-12-01

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

Characterizing Phase Transitions in a Model of Neutral Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Scott, Adam; King, Dawn; Bahar, Sonya

2013-03-01

An evolutionary model was recently introduced for sympatric, phenotypic evolution over a variable fitness landscape with assortative mating (Dees & Bahar 2010). Organisms in the model are described by coordinates in a two-dimensional phenotype space, born at random coordinates with limited variation from their parents as determined by a mutation parameter, mutability. The model has been extended to include both neutral evolution and asexual reproduction in Scott et al (submitted). It has been demonstrated that a second order, non-equilibrium phase transition occurs for the temporal dynamics as the mutability is varied, for both the original model and for neutral conditions. This transition likely belongs to the directed percolation universality class. In contrast, the spatial dynamics of the model shows characteristics of an ordinary percolation phase transition. Here, we characterize the phase transitions exhibited by this model by determining critical exponents for the relaxation times, characteristic lengths, and cluster (species) mass distributions. Missouri Research Board; J.S. McDonnell Foundation

Blow-up and symmetry of sign-changing solutions to some critical elliptic equations

NASA Astrophysics Data System (ADS)

Ben Ayed, Mohamed; El Mehdi, Khalil; Pacella, Filomena

In this paper we continue the analysis of the blow-up of low energy sign-changing solutions of semi-linear elliptic equations with critical Sobolev exponent, started in [M. Ben Ayed, K. El Mehdi, F. Pacella, Blow-up and nonexistence of sign-changing solutions to the Brezis-Nirenberg problem in dimension three, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press]. In addition we prove axial symmetry results for the same kind of solutions in a ball.

TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

NASA Astrophysics Data System (ADS)

Meurice, Y.

2007-06-01

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).

One-dimensional long-range percolation: A numerical study

NASA Astrophysics Data System (ADS)

Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.

2017-07-01

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 <σ <1 are reported. Our analysis is in agreement, up to a numerical precision ≈10-3 , with the mean-field result for the anomalous dimension η =2 -σ , showing that there is no correction to η due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ =1 and from the ɛ -expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .

Water-network percolation transitions in hydrated yeast

NASA Astrophysics Data System (ADS)

Sokołowska, Dagmara; Król-Otwinowska, Agnieszka; Mościcki, Józef K.

2004-11-01

We discovered two percolation processes in succession in dc conductivity of bulk baker’s yeast in the course of dehydration. Critical exponents characteristic for the three-dimensional network for heavily hydrated system, and two dimensions in the light hydration limit, evidenced a dramatic change of the water network dimensionality in the dehydration process.

Anisotropic magnetic properties of the ferromagnetic semiconductor CrSbSe3

NASA Astrophysics Data System (ADS)

Kong, Tai; Stolze, Karoline; Ni, Danrui; Kushwaha, Satya K.; Cava, Robert J.

2018-01-01

Single crystals of CrSbSe3, a structurally pseudo-one-dimensional ferromagnetic semiconductor, were grown using a high-temperature solution growth technique and were characterized by x-ray diffraction, anisotropic temperature- and field-dependent magnetization, temperature-dependent resistivity, and optical absorption measurements. A band gap of 0.7 eV was determined from both resistivity and optical measurements. At high temperatures, CrSbSe3 is paramagnetic and isotropic, with a Curie-Weiss temperature of ˜145 K and an effective moment of ˜4.1 μB /Cr. A ferromagnetic transition occurs at Tc=71 K. The a axis, perpendicular to the chains in the structure, is the magnetic easy axis, while the chain axis direction, along b , is the hard axis. Magnetic isotherms measured around Tc do not follow the behavior predicted by simple mean-field critical exponents for a second-order phase transition. A tentative set of critical exponents is estimated based on a modified Arrott plot analysis, giving β ˜0.25 , γ ˜1.38 , and δ ˜6.6 .

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Relaxation Property and Stability Analysis of the Quasispecies Models

NASA Astrophysics Data System (ADS)

Feng, Xiao-Li; Li, Yu-Xiao; Gu, Jian-Zhong; Zhuo, Yi-Zhong

2009-10-01

The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and second-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error (mutation) threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Eigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.

Breathing modes of Kolumbo submarine volcano (Santorini, Greece).

PubMed

Bakalis, Evangelos; Mertzimekis, Theo J; Nomikou, Paraskevi; Zerbetto, Francesco

2017-04-13

Submarine volcanoes, such as Kolumbo (Santorini, Greece) are natural laboratories for fostering multidisciplinary studies. Their investigation requires the most innovative marine technology together with advanced data analysis. Conductivity and temperature of seawater were recorded directly above Kolumbo's hydrothermal vent system. The respective time series have been analyzed in terms of non-equilibrium techniques. The energy dissipation of the volcanic activity is monitored by the temperature variations of seawater. The venting dynamics of chemical products is monitored by water conductivity. The analysis of the time series in terms of stochastic processes delivers scaling exponents with turning points between consecutive regimes for both conductivity and temperature. Changes of conductivity are shown to behave as a universal multifractal and their variance is subdiffusive as the scaling exponents indicate. Temperature is constant over volcanic rest periods and a universal multifractal behavior describes its changes in line with a subdiffusive character otherwise. The universal multifractal description illustrates the presence of non-conservative conductivity and temperature fields showing that the system never retains a real equilibrium state. The existence of a repeated pattern of the combined effect of both seawater and volcanic activity is predicted. The findings can shed light on the dynamics of chemical products emitted from the vents and point to the presence of underlying mechanisms that govern potentially hazardous, underwater volcanic environments.

Breathing modes of Kolumbo submarine volcano (Santorini, Greece)

NASA Astrophysics Data System (ADS)

Bakalis, Evangelos; Mertzimekis, Theo J.; Nomikou, Paraskevi; Zerbetto, Francesco

2017-04-01

Submarine volcanoes, such as Kolumbo (Santorini, Greece) are natural laboratories for fostering multidisciplinary studies. Their investigation requires the most innovative marine technology together with advanced data analysis. Conductivity and temperature of seawater were recorded directly above Kolumbo’s hydrothermal vent system. The respective time series have been analyzed in terms of non-equilibrium techniques. The energy dissipation of the volcanic activity is monitored by the temperature variations of seawater. The venting dynamics of chemical products is monitored by water conductivity. The analysis of the time series in terms of stochastic processes delivers scaling exponents with turning points between consecutive regimes for both conductivity and temperature. Changes of conductivity are shown to behave as a universal multifractal and their variance is subdiffusive as the scaling exponents indicate. Temperature is constant over volcanic rest periods and a universal multifractal behavior describes its changes in line with a subdiffusive character otherwise. The universal multifractal description illustrates the presence of non-conservative conductivity and temperature fields showing that the system never retains a real equilibrium state. The existence of a repeated pattern of the combined effect of both seawater and volcanic activity is predicted. The findings can shed light on the dynamics of chemical products emitted from the vents and point to the presence of underlying mechanisms that govern potentially hazardous, underwater volcanic environments.

Mott metal-insulator transition on compressible lattices.

PubMed

Zacharias, Mario; Bartosch, Lorenz; Garst, Markus

2012-10-26

The critical properties of the finite temperature Mott end point are drastically altered by a coupling to crystal elasticity, i.e., whenever it is amenable to pressure tuning. Similar as for critical piezoelectric ferroelectrics, the Ising criticality of the electronic system is preempted by an isostructural instability, and long-range shear forces suppress microscopic fluctuations. As a result, the end point is governed by Landau criticality. Its hallmark is, thus, a breakdown of Hooke's law of elasticity with a nonlinear strain-stress relation characterized by a mean-field exponent. Based on a quantitative estimate, we predict critical elasticity to dominate the temperature range ΔT*/T(c)≃8%, close to the Mott end point of κ-(BEDT-TTF)(2)X.

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka

2018-03-01

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

Evidence for criticality in financial data

NASA Astrophysics Data System (ADS)

Ruiz, G.; de Marcos, A. F.

2018-01-01

We provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales Δt. Such cumulative distributions, in accordance with a variety of complex - and financial - systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely ( q, β), that are uniquely defined by Δt. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory

NASA Astrophysics Data System (ADS)

Evans, Robert; Stewart, Maria C.; Wilding, Nigel B.

2017-07-01

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν∥, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory.

PubMed

Evans, Robert; Stewart, Maria C; Wilding, Nigel B

2017-07-28

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν ∥ , which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields.

PubMed

Gandikota, G; Chatain, D; Amiroudine, S; Lyubimova, T; Beysens, D

2014-01-01

The frozen-wave instability which appears at a liquid-vapor interface when a harmonic vibration is applied in a direction tangential to it has been less studied until now. The present paper reports experiments on hydrogen (H2) in order to study this instability when the temperature is varied near its critical point for various gravity levels. Close to the critical point, a liquid-vapor density difference and surface tension can be continuously varied with temperature in a scaled, universal way. The effect of gravity on the height of the frozen waves at the interface is studied by performing the experiments in a magnetic facility where effective gravity that results from the coupling of the Earth's gravity and magnetic forces can be varied. The stability diagram of the instability is obtained. The experiments show a good agreement with an inviscid model [Fluid Dyn. 21 849 (1987)], irrespective of the gravity level. It is observed in the experiments that the height of the frozen waves varies weakly with temperature and increases with a decrease in the gravity level, according to a power law with an exponent of 0.7. It is concluded that the wave height becomes of the order of the cell size as the gravity level is asymptotically decreased to zero. The interface pattern thus appears as a bandlike pattern of alternate liquid and vapor phases, a puzzling phenomenon that was observed with CO2 and H2 near their critical point in weightlessness [Acta Astron. 61 1002 (2007); Europhys. Lett. 86 16003 (2009)].

Pairing transition, coherence transition, and the irreversibility line in granular GdBa2Cu3O7-δ

NASA Astrophysics Data System (ADS)

Roa-Rojas, J.; Menegotto Costa, R.; Pureur, P.; Prieto, P.

2000-05-01

We report on electrical magnetoconductivity experiments near the superconducting transition of a granular sample of GdBa2Cu3O7-δ. The measurements were performed in magnetic fields ranging from 0 to 500 Oe applied parallel to the current orientation. The results show that the transition proceeds in two steps. When the temperature is decreased we first observe the pairing transition, which stabilizes superconductivity within the grains at a temperature practically coincident with the bulk critical temperature Tc. Analysis of the fluctuation contributions to the conductivity shows that the universality class for this transition is that of the three dimensional (3D)-XY model in the ordered case, with dynamic critical exponent z=3/2. Close to the zero-resistance state, the measurements reveal the occurrence of a coherence transition, where the phases of the order parameter in individual grains become long-range ordered. The critical temperature Tco for this transition is close to the point where the resistivity vanishes. A strong enlargement of the fluctuation interval preceding the coherence transition is caused by the applied magnetic field. In this region, a 3D-Gaussian regime and an asymptotic critical regime were clearly identified. The critical conductivity behavior for the coherence transition is interpreted within a 3D-XY model where disorder and frustration are relevant. The irreversibility line is determined from magnetoconductivity measurements performed according to the zero-field-cooled (ZFC) and field-cooled data collected on cooling (FCC) recipes. The locus of this line coincides with the upper temperature limit for the fluctuation region above the coherence transition. The irreversibility line is interpreted as an effect of the formation of small clusters with closed loops of Josephson-coupled grains.

Numerical analysis of the Anderson localization

NASA Astrophysics Data System (ADS)

Markoš, P.

2006-10-01

The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d, ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electron-electron interaction and incoherent scattering are discussed in the paper.

Well-being and consumer culture: a different kind of public health problem?

PubMed

Carlisle, Sandra; Hanlon, Phil

2007-09-01

The concept of well-being is now of interest to many disciplines; as a consequence, it presents an increasingly complex and contested territory. We suggest that much current thinking about well-being can be summarized in terms of four main discourses: scientific, popular, critical and environmental. Exponents of the scientific discourse argue that subjective well-being is now static or declining in developed countries: a paradox for economists, as incomes have grown considerably. Psychological observations on the loss of subjective well-being have also entered popular awareness, in simplified form, and conceptions of well-being as happiness are now influencing contemporary political debate and policy-making. These views have not escaped criticism. Philosophers understand well-being as part of a flourishing human life, not just happiness. Some social theorists critique the export of specific cultural concepts of well-being as human universals. Others view well-being as a potentially divisive construct that may contribute to maintaining social inequalities. Environmentalists argue that socio-cultural patterns of over-consumption, within the neo-liberal economies of developed societies, present an impending ecological threat to individual, social and global well-being. As the four discourses carry different implications for action, we conclude by considering their varied utility and applicability for health promotion.

The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization.

PubMed

West, Geoffrey B; Brown, James H

2005-05-01

Life is the most complex physical phenomenon in the Universe, manifesting an extraordinary diversity of form and function over an enormous scale from the largest animals and plants to the smallest microbes and subcellular units. Despite this many of its most fundamental and complex phenomena scale with size in a surprisingly simple fashion. For example, metabolic rate scales as the 3/4-power of mass over 27 orders of magnitude, from molecular and intracellular levels up to the largest organisms. Similarly, time-scales (such as lifespans and growth rates) and sizes (such as bacterial genome lengths, tree heights and mitochondrial densities) scale with exponents that are typically simple powers of 1/4. The universality and simplicity of these relationships suggest that fundamental universal principles underly much of the coarse-grained generic structure and organisation of living systems. We have proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimised by the process of natural selection. We show how these general constraints explain quarter power scaling and lead to a quantitative, predictive theory that captures many of the essential features of diverse biological systems. Examples considered include animal circulatory systems, plant vascular systems, growth, mitochondrial densities, and the concept of a universal molecular clock. Temperature considerations, dimensionality and the role of invariants are discussed. Criticisms and controversies associated with this approach are also addressed.

Observations of Aerosol Optical Properties over 15 AERONET Sites in Southeast Asia

NASA Astrophysics Data System (ADS)

Chan, J. D.; Lagrosas, N.; Uy, S. N.; Holben, B. N.; Dorado, S.; Tobias, V., Jr.; Anh, N. X.; Po-Hsiung, L.; Janjai, S.; Salinas Cortijo, S. V.; Liew, S. C.; Lim, H. S.; Lestari, P.

2014-12-01

Mean column-integrated optical properties from ground sun photometers of the Aerosol Robotic Network (AERONET) are studied to provide an overview of the characteristics of aerosols over the region as part of the 7 Southeast Asian Studies (7-SEAS) mission. The 15 AERONET sites with the most available level 2 data products are selected from Thailand (Chiang Mai, Mukdahan, Songkhla and Silpakorn University), Malaysia (University Sains Malaysia), Laos (Vientiane), Vietnam (Bac Giang, Bac Lieu and Nha Trang), Taiwan (National Cheng Kung University and Central Weather Bureau Taipei), Singapore, Indonesia (Bandung) and the Philippines (Manila Observatory and Notre Dame of Marbel University). For all 15 sites, high angstrom exponent values (α>1) have been observed. Chiang Mai and USM have the highest mean Angstrom exponent indicating the dominance of fine particles that can be ascribed to biomass burning and urbanization. Sites with the lowest Angstrom exponent values include Bac Lieu (α=1.047) and Manila Observatory (α=1.021). From the average lognormal size distribution curves, Songkhla and NDMU show the smallest annual variation in the fine mode region, indicating the observed fine aerosols are local to the sites. The rest of the sites show high variation which could be due to large scale forcings (e.g., monsoons and biomass burnings) that affect aerosol properties in these sites. Both high and low single scattering albedo at 440 nm (ω0440) values are found in sites located in major urban areas. Silpakorn University, Manila Observatory and Vientiane have all mean ω0440 < 0.90. Singapore and CWB Taipei have ω0440 > 0.94. The discrepancy in ω0 suggests different types of major emission sources present in urban areas. The absorptivity of urban aerosols can vary depending on the strength of traffic emissions, types of fuel combusted and automobile engines used, and the effect of biomass burning aerosols during the dry season. High aerosol optical depth values (τa550 > 0.4) are mainly found over inland sites north of Songkhla and south of China on mainland Asia. Major pollution types in the region include biomass burning smoke and urban aerosols. The highest average τa550 is measured in Bac Giang, which has been studied to be greatly affected by aerosol sources from Eastern China during the later parts of the year.

Competition of density waves and quantum multicritical behavior in Dirac materials from functional renormalization

NASA Astrophysics Data System (ADS)

Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.

2016-03-01

We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.

On the universality of power laws for tokamak plasma predictions

NASA Astrophysics Data System (ADS)

Garcia, J.; Cambon, D.; Contributors, JET

2018-02-01

Significant deviations from well established power laws for the thermal energy confinement time, obtained from extensive databases analysis as the IPB98(y,2), have been recently reported in dedicated power scans. In order to illuminate the adequacy, validity and universality of power laws as tools for predicting plasma performance, a simplified analysis has been carried out in the framework of a minimal modeling for heat transport which is, however, able to account for the interplay between turbulence and collinear effects with the input power known to play a role in experiments with significant deviations from such power laws. Whereas at low powers, the usual scaling laws are recovered with little influence of other plasma parameters, resulting in a robust power low exponent, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q-profile or even the sampling or the number of points considered due to highly non-linear behavior of the heat transport. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law might be intrinsically invalid. Therefore plasma predictions with a power law approximation with a constant exponent obtained from a regression of a broad range of powers and other plasma parameters which can non-linearly affect and suppress heat transport, can lead to misleading results suggesting that this approach should be taken cautiously and its results continuously compared with modeling which can properly capture the underline physics, as gyrokinetic simulations.

Outbreak statistics and scaling laws for externally driven epidemics.

PubMed

Singh, Sarabjeet; Myers, Christopher R

2014-04-01

Power-law scalings are ubiquitous to physical phenomena undergoing a continuous phase transition. The classic susceptible-infectious-recovered (SIR) model of epidemics is one such example where the scaling behavior near a critical point has been studied extensively. In this system the distribution of outbreak sizes scales as P(n)∼n-3/2 at the critical point as the system size N becomes infinite. The finite-size scaling laws for the outbreak size and duration are also well understood and characterized. In this work, we report scaling laws for a model with SIR structure coupled with a constant force of infection per susceptible, akin to a "reservoir forcing". We find that the statistics of outbreaks in this system fundamentally differ from those in a simple SIR model. Instead of fixed exponents, all scaling laws exhibit tunable exponents parameterized by the dimensionless rate of external forcing. As the external driving rate approaches a critical value, the scale of the average outbreak size converges to that of the maximal size, and above the critical point, the scaling laws bifurcate into two regimes. Whereas a simple SIR process can only exhibit outbreaks of size O(N1/3) and O(N) depending on whether the system is at or above the epidemic threshold, a driven SIR process can exhibit a richer spectrum of outbreak sizes that scale as O(Nξ), where ξ∈(0,1]∖{2/3} and O((N/lnN)2/3) at the multicritical point.

Critical behavior near the ferromagnetic phase transition in double perovskite Nd2NiMnO6

NASA Astrophysics Data System (ADS)

Ali, Anzar; Sharma, G.; Singh, Yogesh

2018-05-01

The knowledge of critical exponents plays a crucial role in trying to understand the interaction mechanism near a phase transition. In this report, we present a detailed study of the critical behaviour near the ferromagnetic (FM) transition (TC ˜ 193 K) in Nd2NiMnO6 using the temperature and magnetic field dependent isothermal magnetisation measurements. We used various analysis methods such as Arrott plot, modified Arrott plot, and Kouvel-Fisher plot to estimate the critical parameters. The magnetic critical parameters β = 0.49±0.02, γ = 1.05±0.04 and critical isothermal parameter δ = 3.05±0.02 are in excellent agreement with Widom scaling. The critical parameters analysis emphasizes that mean field interaction is the mechanism driving the FM transition in Nd2NiMnO6.

Zero-temperature directed polymer in random potential in 4+1 dimensions.

PubMed

Kim, Jin Min

2016-12-01

Zero-temperature directed polymer in random potential in 4+1 dimensions is described. The fluctuation ΔE(t) of the lowest energy of the polymer varies as t^{β} with β=0.159±0.007 for polymer length t and ΔE follows ΔE(L)∼L^{α} at saturation with α=0.275±0.009, where L is the system size. The dynamic exponent z≈1.73 is obtained from z=α/β. The estimated values of the exponents satisfy the scaling relation α+z=2 very well. We also monitor the end to end distance of the polymer and obtain z independently. Our results show that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than d=4+1 dimensions.

Silicon dioxide space coatings studied ellipsometrically

NASA Technical Reports Server (NTRS)

De, Bhola N.; Zhao, Yong; Hruska, Jane; Peterkin, Jane; Woollam, John A.

1990-01-01

Mechanisms of initial oxidation of silicon for the formation of silicon dioxide have been investigated. The oxidation of silicon in an atomic oxigen plasma environment is found to exhibit two distinct and linear oxide growth curves for each of the plasma powers used in ashing (25, 50, and 100 watts). Data obtained indicate that the exponent to the pressure in the oxide growth rate formula changes from 1.4 + or - 0.1 to 0.7 + or - 0.1 as one crosses the critical thickness. These data contradict the theory predicting that this exponent should be 1 for both regimes. The activation energy for oxidation in the zone reaction regime is found to be 0.17 eV, in contrast to the published value of 1-2 eV for thermally grown oxides.

Measurement and Statistics of Application Business in Complex Internet

NASA Astrophysics Data System (ADS)

Wang, Lei; Li, Yang; Li, Yipeng; Wu, Shuhang; Song, Shiji; Ren, Yong

Owing to independent topologies and autonomic routing mechanism, the logical networks formed by Internet application business behavior cause the significant influence on the physical networks. In this paper, the backbone traffic of TUNET (Tsinghua University Networks) is measured, further more, the two most important application business: HTTP and P2P are analyzed at IP-packet level. It is shown that uplink HTTP and P2P packets behavior presents spatio-temporal power-law characteristics with exponents 1.25 and 1.53 respectively. Downlink HTTP packets behavior also presents power-law characteristics, but has more little exponents γ = 0.82 which differs from traditional complex networks research result. Moreover, downlink P2P packets distribution presents an approximate power-law which means that flow equilibrium profits little from distributed peer-to peer mechanism actually.

Scaling of Directed Dynamical Small-World Networks with Random Responses

NASA Astrophysics Data System (ADS)

Zhu, Chen-Ping; Xiong, Shi-Jie; Tian, Ying-Jie; Li, Nan; Jiang, Ke-Sheng

2004-05-01

A dynamical model of small-world networks, with directed links which describe various correlations in social and natural phenomena, is presented. Random responses of sites to the input message are introduced to simulate real systems. The interplay of these ingredients results in the collective dynamical evolution of a spinlike variable S(t) of the whole network. The global average spreading length s and average spreading time s are found to scale as p-αln(N with different exponents. Meanwhile, S(t) behaves in a duple scaling form for N≫N*: S˜f(p-βqγt˜), where p and q are rewiring and external parameters, α, β, and γ are scaling exponents, and f(t˜) is a universal function. Possible applications of the model are discussed.

Probing the role of long-range interactions in the dynamics of a long-range Kitaev chain

NASA Astrophysics Data System (ADS)

Dutta, Anirban; Dutta, Amit

2017-09-01

We study the role of long-range interactions (more precisely, the long-range superconducting gap term) on the nonequilibrium dynamics considering a long-range p -wave superconducting chain in which the superconducting term decays with distance between two sites in a power-law fashion characterized by an exponent α . We show that the Kibble-Zurek scaling exponent, dictating the power-law decay of the defect density in the final state reached following a slow (in comparison to the time scale associated with the minimum gap in the spectrum of the Hamiltonian) quenching of the chemical potential μ across a quantum critical point, depends nontrivially on the exponent α as long as α <2 ; on the other hand, for α >2 , we find that the exponent saturates to the corresponding well-known value of 1 /2 expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the nonanalyticities in the rate function of the return possibility I (t ) in subsequent temporal evolution following a sudden change in μ , we show the existence of a new region; in this region, we find three instants of cusp singularities in I (t ) associated with a single sector of Fisher zeros. Notably, the width of this region shrinks as α increases and vanishes in the limit α →2 , indicating that this special region is an artifact of the long-range nature of the Hamiltonian.

Maximum Rate of Growth of Enstrophy in Solutions of the Fractional Burgers Equation

NASA Astrophysics Data System (ADS)

Yun, Dongfang; Protas, Bartosz

2018-02-01

This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the classical and fractional enstrophy in the fractional Burgers equation in the subcritical and supercritical regimes. Since solutions to this equation exhibit, respectively, globally well-posed behavior and finite-time blowup in these two regimes, this makes it a useful model to study the maximum instantaneous growth of enstrophy possible in these two distinct situations. First, we obtain estimates on the rates of growth and then show that these estimates are sharp up to numerical prefactors. This is done by numerically solving suitably defined constrained maximization problems and then demonstrating that for different values of the fractional dissipation exponent the obtained maximizers saturate the upper bounds in the estimates as the enstrophy increases. We conclude that the power-law dependence of the enstrophy rate of growth on the fractional dissipation exponent has the same global form in the subcritical, critical and parts of the supercritical regime. This indicates that the maximum enstrophy rate of growth changes smoothly as global well-posedness is lost when the fractional dissipation exponent attains supercritical values. In addition, nontrivial behavior is revealed for the maximum rate of growth of the fractional enstrophy obtained for small values of the fractional dissipation exponents. We also characterize the structure of the maximizers in different cases.

Nanoscale morphogenesis of nylon-sputtered plasma polymer particles

NASA Astrophysics Data System (ADS)

Choukourov, Andrei; Shelemin, Artem; Pleskunov, Pavel; Nikitin, Daniil; Khalakhan, Ivan; Hanuš, Jan

2018-05-01

Sub-micron polymer particles are highly important in various fields including astrophysics, thermonuclear fusion and nanomedicine. Plasma polymerization offers the possibility to produce particles with tailor-made size, crosslink density and chemical composition to meet the requirements of a particular application. However, the mechanism of nucleation and growth of plasma polymer particles as well as diversity of their morphology remain far from being clear. Here, we prepared nitrogen-containing plasma polymer particles by rf magnetron sputtering of nylon in a gas aggregation cluster source with variable length. The method allowed the production of particles with roughly constant chemical composition and number density but with the mean size changing from 80 to 320 nm. Atomic Force Microscopy with super-sharp probes was applied to study the evolution of the particle surface topography as they grow in size. Height–height correlation and power spectral density functions were obtained to quantify the roughness exponent α  =  0.78, the growth exponent β  =  0.35, and the dynamic exponent 1/z  =  0.50. The set of critical exponents indicates that the particle surface evolves in a self-affine mode and the overall particle growth is caused by the accretion of polymer-forming species from the gas phase and not by coagulation. Redistribution of the incoming material over the surface coupled with the inhomogeneous distribution of inner stress is suggested as the main factor that determines the morphogenesis of the plasma polymer particles.

Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model

NASA Astrophysics Data System (ADS)

Mankin, Romi; Paekivi, Sander

2018-01-01

The behavior of a stochastic resonate-and-fire neuron model based on a reduction of a fractional noise-driven generalized Langevin equation (GLE) with a power-law memory kernel is considered. The effect of temporally correlated random activity of synaptic inputs, which arise from other neurons forming local and distant networks, is modeled as an additive fractional Gaussian noise in the GLE. Using a first-passage-time formulation, in certain system parameter domains exact expressions for the output interspike interval (ISI) density and for the survival probability (the probability that a spike is not generated) are derived and their dependence on input parameters, especially on the memory exponent, is analyzed. In the case of external white noise, it is shown that at intermediate values of the memory exponent the survival probability is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonancelike suppression of the probability of spike generation as a function of the memory exponent. Moreover, an examination of the dependence of multimodality in the ISI distribution on input parameters shows that there exists a critical memory exponent αc≈0.402 , which marks a dynamical transition in the behavior of the system. That phenomenon is illustrated by a phase diagram describing the emergence of three qualitatively different structures of the ISI distribution. Similarities and differences between the behavior of the model at internal and external noises are also discussed.

Electromigration kinetics and critical current of Pb-free interconnects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Minhua; Rosenberg, Robert

2014-04-07

Electromigration kinetics of Pb-free solder bump interconnects have been studied using a single bump parameter sweep technique. By removing bump to bump variations in structure, texture, and composition, the single bump sweep technique has provided both activation energy and power exponents that reflect atomic migration and interface reactions with fewer samples, shorter stress time, and better statistics than standard failure testing procedures. Contact metallurgies based on Cu and Ni have been studied. Critical current, which corresponds to the Blech limit, was found to exist in the Ni metallurgy, but not in the Cu metallurgy. A temperature dependence of critical currentmore » was also observed.« less

Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models.

PubMed

Azeyanagi, Tatsuo; Ferrari, Frank; Massolo, Fidel I Schaposnik

2018-02-09

We study the Schwinger-Dyson equations of a fermionic planar matrix quantum mechanics [or tensor and Sachdev-Ye-Kitaev (SYK) models] at leading melonic order. We find two solutions describing a high entropy, SYK black-hole-like phase and a low entropy one with trivial IR behavior. There is a line of first order phase transitions that terminates at a new critical point. Critical exponents are nonmean field and differ on the two sides of the transition. Interesting phenomena are also found in unstable and stable bosonic models, including Kazakov critical points and inconsistency of SYK-like solutions of the IR limit.

Application of the coherent anomaly method to percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

1988-03-01

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold pc and critical exponents. We obtain pc=0.589, β=0.140, γ=2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Application of the Coherent Anomaly Method to Percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold ϱc and critical exponents. We obtain pc = 0.589, Β=0.140, Γ = 2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Universal scaling law in human behavioral organization.

PubMed

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R; Yamamoto, Yoshiharu

2007-09-28

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

Universality in chaos: Lyapunov spectrum and random matrix theory.

PubMed

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t=0, while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Universal Scaling Law in Human Behavioral Organization

NASA Astrophysics Data System (ADS)

Nakamura, Toru; Kiyono, Ken; Yoshiuchi, Kazuhiro; Nakahara, Rika; Struzik, Zbigniew R.; Yamamoto, Yoshiharu

2007-09-01

We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression.

Universality in chaos: Lyapunov spectrum and random matrix theory

NASA Astrophysics Data System (ADS)

Hanada, Masanori; Shimada, Hidehiko; Tezuka, Masaki

2018-02-01

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of a stringy black hole and the mass-deformed models. The massless limit, which has a dual string theory interpretation, is special in that the universal behavior can be seen already at t =0 , while in other cases it sets in at late time. The same pattern is demonstrated also in the product of random matrices.

Critical behavior in graphene with Coulomb interactions.

PubMed

Wang, Jianhui; Fertig, H A; Murthy, Ganpathy

2010-05-07

We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Potts Model in One-Dimension on Directed Small-World Networks

NASA Astrophysics Data System (ADS)

Aquino, Édio O.; Lima, F. W. S.; Araújo, Ascânio D.; Costa Filho, Raimundo N.

2018-06-01

The critical properties of the Potts model with q=3 and 8 states in one-dimension on directed small-world networks are investigated. This disordered system is simulated by updating it with the Monte Carlo heat bath algorithm. The Potts model on these directed small-world networks presents in fact a second-order phase transition with a new set of critical exponents for q=3 considering a rewiring probability p=0.1. For q=8 the system exhibits only a first-order phase transition independent of p.

Crossover from isotropic to directed percolation

NASA Astrophysics Data System (ADS)

Zhou, Zongzheng; Yang, Ji; Ziff, Robert M.; Deng, Youjin

2012-08-01

We generalize the directed percolation (DP) model by relaxing the strict directionality of DP such that propagation can occur in either direction but with anisotropic probabilities. We denote the probabilities as p↓=ppd and p↑=p(1-pd), with p representing the average occupation probability and pd controlling the anisotropy. The Leath-Alexandrowicz method is used to grow a cluster from an active seed site. We call this model with two main growth directions biased directed percolation (BDP). Standard isotropic percolation (IP) and DP are the two limiting cases of the BDP model, corresponding to pd=1/2 and pd=0,1 respectively. In this work, besides IP and DP, we also consider the 1/2

Sweeprate and temperature effects on crackling noise

NASA Astrophysics Data System (ADS)

White, Robert Allen

Crackling noise, defined as separate bursts characterized by power law behavior of the frequency histograms over many decades, is observed in many driven systems far from equilibrium. Examples of such systems pepper a remarkable range of length and energy scales from jerky domain wall motion of disordered magnets, to the sometimes devastating crackling of the earth to the bursty release of energy in the photosphere of the sun dwarfing that of our most horrible WMD. Typically, crackling noise is modeled in the infinitely slow driving rate limit at zero temperature. In this dissertation I investigate the effects of relaxing these limits. First I consider the crackling system at zero temperature and finite sweeprate. I discuss how the temporal overlap of power law bursts can account for a wide range of scaling behavior and provide a criterion for sweeprate controlled exponents based on exponents obtained in the infinitely slowly driven limit. I also discuss scaling arguments for hitherto unexplained results in the power spectrum of crackling response in disordered magnets, commonly referred to as Barkhausen noise. Scaling arguments and numerical results are compared to Barkhausen noise measurements in two materials representing distinct adiabatically driven universality classes. Relaxation of the zero temperature constraint cannot be done without considering finite sweeprates due to global relaxation timescales that arise at finite temperatures. We investigate the connection between sweeprate and thermal fluctuations in the far from equilibrium limit typical of crackling systems. Again, using scaling arguments and numerical simulations of the random field Ising model near a disorder-induced critical point we analyze interesting crossover phenomena in the power spectra which are also observed in Barkhausen noise but have yet to be explained.

On the thermodynamic origin of metabolic scaling.

PubMed

Ballesteros, Fernando J; Martinez, Vicent J; Luque, Bartolo; Lacasa, Lucas; Valor, Enric; Moya, Andrés

2018-01-23

The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organism to maintain its metabolism. This balance tunes the shape of an additive model from which different effective scalings can be recovered as particular cases, thereby reconciling previously inconsistent empirical evidence in mammals, birds, insects and even plants under a unified framework. This model is biologically motivated, fits remarkably well the data, and also explains additional features such as the relation between energy lost as heat and mass, the role and influence of different climatic environments or the difference found between endotherms and ectotherms.

dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality

NASA Astrophysics Data System (ADS)

Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele

2018-04-01

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high Tc superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality.

PubMed

Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele

2018-04-27

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

Relaxation phenomena in AOT-water-decane critical and dense microemulsions

NASA Astrophysics Data System (ADS)

Letamendia, L.; Pru-Lestret, E.; Panizza, P.; Rouch, J.; Sciortino, F.; Tartaglia, P.; Hashimoto, C.; Ushiki, H.; Risso, D.

2001-11-01

We report on extensive measurements of the low and high frequencies sound velocity and sound absorption in AOT-water-decane microemulsions deduced from ultrasonic and, for the first time as far as the absorption is concerned, from Brillouin scattering experiments. New experimental results on dielectric relaxation are also reported. Our results, which include data taken for critical as well as dense microemulsions, show new interesting relaxation phenomena. The relaxation frequencies deduced from very high frequency acoustical measurements are in good agreement with new high frequency dielectric relaxation measurements. We show that along the critical isochore, sound dispersion, relaxation frequency, and static dielectric permittivity can be accurately fitted to power laws. The absolute values of the new exponents we derived from experimental data are nearly equal, and they are very close to β=0.33 characterising the shape of the coexistence curve. The exponent characterising the infinite frequency permittivity is very close to 0.04 relevant to the diverging shear viscosity. For dense microemulsions, two well defined relaxation domains have been identified and the temperature variations of the sound absorption and the zero frequency dielectric permittivity bear striking similarities. We also show that the relaxation frequency of the slow relaxation process is almost independent of temperature and volume fraction and so cannot be attributed to percolation phenomena, whereas it can more likely be attributed to an intrinsic relaxation process probably connected to membrane fluctuations.

Heisenberg spin-glass behaviour in Ga0.99Yb0.01FeO3

NASA Astrophysics Data System (ADS)

Neacsa, Daniela Maria; Gruener, Gisèle; Hebert, Sylvie; Soret, Jean-Claude

2017-06-01

The dynamic and static magnetic properties of Ga0.99Yb0.01FeO3 are studied in detail using ac susceptibility and dc magnetization measurements. The study shows that the compound undergoes a spin-glass freezing at Tg ≈ 213 K . The dynamic scaling analysis of ac susceptibility data reveals typical features characteristic of canonical spin-glasses, i.e., relaxation time τ∗ ∼10-14 s , critical exponent νz = 4.1 ± 0.2 , and frequency sensitivity parameter δf ∼10-3 within three frequency decades. The analysis of the critical behaviour of the static nonlinear susceptibility yields the critical exponents γ = 4.3 ± 0.1, β = 1.0 ± 0.1 , and δ = 5.5 ± 0.5 , which lie between those typical of three-dimensional (3D) weakly anisotropic Heisenberg and Ising spin glasses. The analysis of the field-cooled and zero-field-cooled magnetization data allows to define two characteristic temperatures depending on the applied magnetic field. The upper one, Tirr(H) , is the threshold temperature corresponding to the appearance of weak irreversibility, whereas the lower one, Ts(H) , marks the onset of strong irreversibility. The resulting field-temperature phase diagram turns out to be in good quantitative agreement with the mean-field predictions for 3D Heisenberg spin-glass with random magnetic anisotropy, and appears consistent with the chiral driven freezing scenario.

Coexistence of short- and long-range ferromagnetic order in nanocrystalline Fe2Mn1-xCuxAl (x=0.0, 0.1 and 0.3) synthesized by high-energy ball milling

NASA Astrophysics Data System (ADS)

Thanh, Tran Dang; Nanto, Dwi; Tuyen, Ngo Thi Uyen; Nan, Wen-Zhe; Yu, YiKyung; Tartakovsky, Daniel M.; Yu, S. C.

2015-11-01

In this work, we prepared nanocrystalline Fe2Mn1-xCuxAl (x=0.0, 0.1 and 0.3) powders by the high energy ball milling technique, and then studied their critical properties. Our analysis reveals that the increase of Cu-doping concentration (up to x=0.3) in these powders leads to a gradual increase of the ferromagnetic-paramagnetic transition temperature from 406 to 452 K. The Banerjee criterion suggests that all the samples considered undergo a second-order phase transition. A modified Arrott plot and scaling analysis indicate that the critical exponents (β=0.419 and 0.442, γ=1.082 and 1.116 for x=0.0 and 0.1, respectively) are located in between those expected for the 3D-Heisenberg and the mean-field models; the values of β=0.495 and γ=1.046 for x=0.3 sample are very close to those of the mean-field model. These features reveal the coexistence of the short- and long-range ferromagnetic order in the nanocrystalline Fe2Mn1-xCuxAl powders. Particularly, as the concentration of Cu increases, values of the critical exponent shift towards those of the mean-field model. Such results prove the Cu doping favors establishing a long-range ferromagnetic order.

SIR epidemics with long-range infection in one dimension

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2013-04-01

We study epidemic processes with immunization on very large 1-dimensional lattices, where at least some of the infections are non-local, with rates decaying as power laws p(x) ˜ x-σ-1 for large distances x. When starting with a single infected site, the cluster of infected sites stays always bounded if σ > 1 (and dies with probability 1, if its size is allowed to fluctuate down to zero), but the process can lead to an infinite epidemic for σ < 1. For σ < 0 the behavior is essentially of mean-field type, but for 0 < σ ≤ 1 the behavior is non-trivial, both for the critical and for supercritical cases. For critical epidemics we confirm a previous prediction that the critical exponents controlling the correlation time and the correlation length are simply related to each other, and we verify detailed field theoretic predictions for σ↘1/3. For σ = 1 we find generic power laws with continuously varying exponents even in the supercritical case, and confirm in detail the predicted Kosterlitz-Thouless nature of the transition. Finally, the mass N(t) of supercritical clusters grows for 0 < σ < 1 like a stretched exponential. This implies that networks embedded in 1-d space with power-behaved link distributions have infinite intrinsic dimension (based on the graph distance), but are not small world.

Scaling behavior of nonisothermal phase separation.

PubMed

Rüllmann, Max; Alig, Ingo

2004-04-22

The phase separation process in a critical mixture of polydimethylsiloxane and polyethylmethylsiloxane (PDMS/PEMS, a system with an upper critical solution temperature) was investigated by time-resolved light scattering during continuous quenches from the one-phase into the two-phase region. Continuous quenches were realized by cooling ramps with different cooling rates kappa. Phase separation kinetics is studied by means of the temporal evolution of the scattering vector qm and the intensity Im at the scattering peak. The curves qm(t) for different cooling rates can be shifted onto a single mastercurve. The curves Im(t) show similar behavior. As shift factors, a characteristic length Lc and a characteristic time tc are introduced. Both characteristic quantities depend on the cooling rate through power laws: Lc approximately kappa(-delta) and tc approximately kappa(-rho). Scaling behavior in isothermal critical demixing is well known. There the temporal evolutions of qm and Im for different quench depths DeltaT can be scaled with the correlation length xi and the interdiffusion coefficient D, both depending on DeltaT through critical power laws. We show in this paper that the cooling rate scaling in nonisothermal demixing is a consequence of the quench depth scaling in the isothermal case. The exponents delta and rho are related to the critical exponents nu and nu* of xi and D, respectively. The structure growth during nonisothermal demixing can be described with a semiempirical model based on the hydrodynamic coarsening mechanism well known in the isothermal case. In very late stages of nonisothermal phase separation a secondary scattering maximum appears. This is due to secondary demixing. We explain the onset of secondary demixing by a competition between interdiffusion and coarsening. (c) 2004 American Institute of Physics

Superconductivity from a non-Fermi-liquid metal: Kondo fluctuation mechanism in slave-fermion theory

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok

2010-03-01

We propose Kondo fluctuation mechanism of superconductivity, differentiated from the spin-fluctuation theory as the standard model for unconventional superconductivity in the weak-coupling approach. Based on the U(1) slave-fermion representation of an effective Anderson lattice model, where localized spins are described by the Schwinger boson theory and hybridization or Kondo fluctuations weaken antiferromagnetic correlations of localized spins, we found an antiferromagnetic quantum critical point from an antiferromagnetic metal to a heavy-fermion metal in our recent study. The Kondo-induced antiferromagnetic quantum critical point was shown to be described by both conduction electrons and fermionic holons interacting with critical spin fluctuations given by deconfined bosonic spinons with a spin quantum number 1/2. Surprisingly, such critical modes turned out to be described by the dynamical exponent z=3 , giving rise to the well-known non-Fermi-liquid physics such as the divergent Grüneisen ratio with an exponent 2/3 and temperature-linear resistivity in three dimensions. We find that the z=3 antiferromagnetic quantum critical point becomes unstable against superconductivity, where critical spinon excitations give rise to pairing correlations between conduction electrons and between fermionic holons, respectively, via hybridization fluctuations. Such two kinds of pairing correlations result in multigap unconventional superconductivity around the antiferromagnetic quantum critical point of the slave-fermion theory, where s -wave pairing is not favored generically due to strong correlations. We show that the ratio between each superconducting gap for conduction electrons Δc and holons Δf and the transition temperature Tc is 2Δc/Tc˜9 and 2Δf/Tc˜O(10-1) , remarkably consistent with CeCoIn5 . A fingerprint of the Kondo mechanism is emergence of two kinds of resonance modes in not only spin but also charge fluctuations, where the charge resonance mode at an antiferromagnetic wave vector originates from d -wave pairing of spinless holons. We discuss how the Kondo fluctuation theory differs from the spin-fluctuation approach.

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

NASA Astrophysics Data System (ADS)

Tantet, Alexis; Lucarini, Valerio; Dijkstra, Henk A.

2018-02-01

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle-Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.