Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators 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, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

Characteristic power spectrum of diffusive interface dynamics in the two-dimensional Ising model

NASA Astrophysics Data System (ADS)

Masumoto, Yusuke; Takesue, Shinji

2018-05-01

We investigate properties of the diffusive motion of an interface in the two-dimensional Ising model in equilibrium or nonequilibrium situations. We focused on the relation between the power spectrum of a time sequence of spins and diffusive motion of an interface which was already clarified in one-dimensional systems with a nonequilibrium phase transition like the asymmetric simple exclusion process. It is clarified that the interface motion is a diffusion process with a drift force toward the higher-temperature side when the system is in contact with heat reservoirs at different temperatures and heat transfers through the system. Effects of the width of the interface are also discussed.

Dynamic hysteresis in a one-dimensional Ising model: application to allosteric proteins.

PubMed

Graham, I; Duke, T A J

2005-06-01

We solve exactly the problem of dynamic hysteresis for a finite one-dimensional Ising model at low temperature. We find that the area of the hysteresis loop, as the field is varied periodically, scales as the square root of the field frequency for a large range of frequencies. Below a critical frequency there is a correction to the scaling law, resulting in a linear relationship between hysteresis area and frequency. The one-dimensional Ising model provides a simplified description of switchlike behavior in allosteric proteins, such as hemoglobin. Thus our analysis predicts the switching dynamics of allosteric proteins when they are exposed to a ligand concentration which changes with time. Many allosteric proteins bind a regulator that is maintained at a nonequilibrium concentration by active signal transduction processes. In the light of our analysis, we discuss to what extent allosteric proteins can respond to changes in regulator concentration caused by an upstream signaling event, while remaining insensitive to the intrinsic nonequilibrium fluctuations in regulator level which occur in the absence of a signal.

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.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

2011-11-01

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov chain uv sampler

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-09-01

Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing holographic boundary distributions. The main ingredient of the Markov chain Monte Carlo sampler is the invariance under dilation. This paper presents a generalization to higher dimensions with the critical 3D Ising model. This leads to numerical estimations of a subset of the CFT data—scaling weights and structure constants—through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 036, 10.1007/JHEP08(2016)036].

Rényi information flow in the Ising model with single-spin dynamics.

PubMed

Deng, Zehui; Wu, Jinshan; Guo, Wenan

2014-12-01

The n-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.

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.

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.

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.

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.

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.

Shock probes in a one-dimensional Katz-Lebowitz-Spohn model

NASA Astrophysics Data System (ADS)

Chatterjee, Sakuntala; Barma, Mustansir

2008-06-01

We consider shock probes in a one-dimensional driven diffusive medium with nearest-neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterizing the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Ecological risk assessment of TBT in Ise Bay.

PubMed

Yamamoto, Joji; Yonezawa, Yoshitaka; Nakata, Kisaburo; Horiguchi, Fumio

2009-02-01

An ecological risk assessment of tributyltin (TBT) in Ise Bay was conducted using the margin of exposure (MOE) method. The assessment endpoint was defined to protect the survival, growth and reproduction of marine organisms. Sources of TBT in this study were assumed to be commercial vessels in harbors and navigation routes. Concentrations of TBT in Ise Bay were estimated using a three-dimensional hydrodynamic model, an ecosystem model and a chemical fate model. Estimated MOEs for marine organisms for 1990 and 2008 were approximately 0.1-2.0 and over 100 respectively, indicating a declining temporal trend in the probability of adverse effects. The chemical fate model predicts a much longer persistence of TBT in sediments than in the water column. Therefore, it is necessary to monitor the harmful effects of TBT on benthic organisms.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

PubMed

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-10-10

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

PubMed Central

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-01-01

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

The Critical Z-Invariant Ising Model via Dimers: Locality Property

NASA Astrophysics Data System (ADS)

Boutillier, Cédric; de Tilière, Béatrice

2011-01-01

We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher (J Math Phys 7:1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of Kenyon (Invent Math 150(2):409-439, 2002), as a contour integral of the discrete exponential function of Mercat (Discrete period matrices and related topics, 2002) and Kenyon (Invent Math 150(2):409-439, 2002) multiplied by a local function. Using results of Boutillier and de Tilière (Prob Theor Rel Fields 147(3-4):379-413, 2010) and techniques of de Tilière (Prob Th Rel Fields 137(3-4):487-518, 2007) and Kenyon (Invent Math 150(2):409-439, 2002), this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model (Baxter, in Exactly solved models in statistical mechanics, Academic Press, London, 1982), and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in Kenyon (Invent Math 150(2):409-439, 2002).

Simulation of glioblastoma multiforme (GBM) tumor cells using ising model on the Creutz Cellular Automaton

NASA Astrophysics Data System (ADS)

Züleyha, Artuç; Ziya, Merdan; Selçuk, Yeşiltaş; Kemal, Öztürk M.; Mesut, Tez

2017-11-01

Computational models for tumors have difficulties due to complexity of tumor nature and capacities of computational tools, however, these models provide visions to understand interactions between tumor and its micro environment. Moreover computational models have potential to develop strategies for individualized treatments for cancer. To observe a solid brain tumor, glioblastoma multiforme (GBM), we present a two dimensional Ising Model applied on Creutz cellular automaton (CCA). The aim of this study is to analyze avascular spherical solid tumor growth, considering transitions between non tumor cells and cancer cells are like phase transitions in physical system. Ising model on CCA algorithm provides a deterministic approach with discrete time steps and local interactions in position space to view tumor growth as a function of time. Our simulation results are given for fixed tumor radius and they are compatible with theoretical and clinic data.

The Ising Decision Maker: a binary stochastic network for choice response time.

PubMed

Verdonck, Stijn; Tuerlinckx, Francis

2014-07-01

The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (c) 2014 APA, all rights reserved.

On the p, q-binomial distribution and the Ising model

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Rosengren, A.

2010-08-01

We employ p, q-binomial coefficients, a generalisation of the binomial coefficients, to describe the magnetisation distributions of the Ising model. For the complete graph this distribution corresponds exactly to the limit case p = q. We apply our investigation to the simple d-dimensional lattices for d = 1, 2, 3, 4, 5 and fit p, q-binomial distributions to our data, some of which are exact but most are sampled. For d = 1 and d = 5, the magnetisation distributions are remarkably well-fitted by p,q-binomial distributions. For d = 4 we are only slightly less successful, while for d = 2, 3 we see some deviations (with exceptions!) between the p, q-binomial and the Ising distribution. However, at certain temperatures near T c the statistical moments of the fitted distribution agree with the moments of the sampled data within the precision of sampling. We begin the paper by giving results of the behaviour of the p, q-distribution and its moment growth exponents given a certain parameterisation of p, q. Since the moment exponents are known for the Ising model (or at least approximately for d = 3) we can predict how p, q should behave and compare this to our measured p, q. The results speak in favour of the p, q-binomial distribution's correctness regarding its general behaviour in comparison to the Ising model. The full extent to which they correctly model the Ising distribution, however, is not settled.

The influence of further-neighbor spin-spin interaction on a ground state of 2D coupled spin-electron model in a magnetic field

NASA Astrophysics Data System (ADS)

Čenčariková, Hana; Strečka, Jozef; Gendiar, Andrej; Tomašovičová, Natália

2018-05-01

An exhaustive ground-state analysis of extended two-dimensional (2D) correlated spin-electron model consisting of the Ising spins localized on nodal lattice sites and mobile electrons delocalized over pairs of decorating sites is performed within the framework of rigorous analytical calculations. The investigated model, defined on an arbitrary 2D doubly decorated lattice, takes into account the kinetic energy of mobile electrons, the nearest-neighbor Ising coupling between the localized spins and mobile electrons, the further-neighbor Ising coupling between the localized spins and the Zeeman energy. The ground-state phase diagrams are examined for a wide range of model parameters for both ferromagnetic as well as antiferromagnetic interaction between the nodal Ising spins and non-zero value of external magnetic field. It is found that non-zero values of further-neighbor interaction leads to a formation of new quantum states as a consequence of competition between all considered interaction terms. Moreover, the new quantum states are accompanied with different magnetic features and thus, several kinds of field-driven phase transitions are observed.

A unified effective-field renormalization-group framework approach for the quenched diluted Ising models

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Fittipaldi, I. P.

1994-05-01

A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.

Spin waves, vortices, fermions, and duality in the Ising and Baxter models

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

Ogilvie, M.C.

1981-10-15

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex+spin-wave decomposition, that the Z/sub p/-Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.

Entanglement entropy at infinite-randomness fixed points in higher dimensions.

PubMed

Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko

2007-10-05

The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

Nonequilibrium Statistical Mechanics in One Dimension

NASA Astrophysics Data System (ADS)

Privman, Vladimir

2005-08-01

Part I. Reaction-Diffusion Systems and Models of Catalysis; 1. Scaling theories of diffusion-controlled and ballistically-controlled bimolecular reactions S. Redner; 2. The coalescence process, A+A->A, and the method of interparticle distribution functions D. ben-Avraham; 3. Critical phenomena at absorbing states R. Dickman; Part II. Kinetic Ising Models; 4. Kinetic ising models with competing dynamics: mappings, correlations, steady states, and phase transitions Z. Racz; 5. Glauber dynamics of the ising model N. Ito; 6. 1D Kinetic ising models at low temperatures - critical dynamics, domain growth, and freezing S. Cornell; Part III. Ordering, Coagulation, Phase Separation; 7. Phase-ordering dynamics in one dimension A. J. Bray; 8. Phase separation, cluster growth, and reaction kinetics in models with synchronous dynamics V. Privman; 9. Stochastic models of aggregation with injection H. Takayasu and M. Takayasu; Part IV. Random Sequential Adsorption and Relaxation Processes; 10. Random and cooperative sequential adsorption: exactly solvable problems on 1D lattices, continuum limits, and 2D extensions J. W. Evans; 11. Lattice models of irreversible adsorption and diffusion P. Nielaba; 12. Deposition-evaporation dynamics: jamming, conservation laws and dynamical diversity M. Barma; Part V. Fluctuations In Particle and Surface Systems; 13. Microscopic models of macroscopic shocks S. A. Janowsky and J. L. Lebowitz; 14. The asymmetric exclusion model: exact results through a matrix approach B. Derrida and M. R. Evans; 15. Nonequilibrium surface dynamics with volume conservation J. Krug; 16. Directed walks models of polymers and wetting J. Yeomans; Part VI. Diffusion and Transport In One Dimension; 17. Some recent exact solutions of the Fokker-Planck equation H. L. Frisch; 18. Random walks, resonance, and ratchets C. R. Doering and T. C. Elston; 19. One-dimensional random walks in random environment K. Ziegler; Part VII. Experimental Results; 20. Diffusion-limited exciton kinetics in one-dimensional systems R. Kroon and R. Sprik; 21. Experimental investigations of molecular and excitonic elementary reaction kinetics in one-dimensional systems R. Kopelman and A. L. Lin; 22. Luminescence quenching as a probe of particle distribution S. H. Bossmann and L. S. Schulman; Index.

A Short Note on the Scaling Function Constant Problem in the Two-Dimensional Ising Model

NASA Astrophysics Data System (ADS)

Bothner, Thomas

2018-02-01

We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297-311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697-721, 1998) using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058-1092, 1977).

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

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

Intraoperative 3D Navigation for Single or Multiple 125I-Seed Localization in Breast-Preserving Cancer Surgery.

PubMed

Pouw, Bas; de Wit-van der Veen, Linda J; van Duijnhoven, Frederieke; Rutgers, Emiel J Th; Stokkel, Marcel P M; Valdés Olmos, Renato A; Vrancken Peeters, Marie-Jeanne T F D

2016-05-01

Mammographic screening has led to the identification of more women with nonpalpable breast cancer, many of them to be treated with breast-preserving surgery. To accomplish radical tumor excision, adequate localization techniques such as radioactive seed localization (RSL) are required. For RSL, a radioactive I-seed is implanted central in the tumor to enable intraoperative localization using a γ-probe. In case of extensive tumor or multifocal carcinoma, multiple I-seeds can be used to delineate the involved area. Preoperative imaging is performed different from surgical positioning; therefore, exact I-seed depth remains unknown during surgery. Twenty patients (mean age, 56.8 years) with 25 implanted I-seeds scheduled for RSL were included. Sixteen patients had 1 I-seed implanted in the primary lesion, 3 patients had 2 I-seeds, and 1 patient had 3 I-seeds. Freehand SPECT localized I-seeds by measuring γ-counts from different directions, all registered by an optical tracking system. A reconstruction and visualization algorithm enabled 3-dimensional (3D) navigation toward the I-seeds. Freehand SPECT visualized all I-seeds in primary tumors and provided preincision depth information. The deviation, mean (SD), between the freehand SPECT depth and the surgical depth estimation was 1.9 (2.1) mm (range, 0-7 mm). Three-dimensional freehand SPECT was especially useful identifying multiple implanted I-seeds because the conventional γ-probe has more difficulty discriminating I-seeds transcutaneous. Freehand SPECT with 3D navigation is a valuable tool in RSL for both single and multiple implanted I-seeds in breast-preserving cancer surgery. Freehand SPECT provides continuous updating 3D imaging with information about depth and location of the I-seeds contributing to adequate excision of nonpalpable breast cancer.

Chiral Tricritical Point: A New Universality Class in Dirac Systems

NASA Astrophysics Data System (ADS)

Yin, Shuai; Jian, Shao-Kai; Yao, Hong

2018-05-01

Tricriticality, as a sister of criticality, is a fundamental and absorbing issue in condensed-matter physics. It has been verified that the bosonic Wilson-Fisher universality class can be changed by gapless fermionic modes at criticality. However, the counterpart phenomena at tricriticality have rarely been explored. In this Letter, we study a model in which a tricritical Ising model is coupled to massless Dirac fermions. We find that the massless Dirac fermions result in the emergence of a new tricritical point, which we refer to as the chiral tricritical point (CTP), at the phase boundary between the Dirac semimetal and the charge-density wave insulator. From functional renormalization group analysis of the effective action, we obtain the critical behaviors of the CTP, which are qualitatively distinct from both the tricritical Ising universality and the chiral Ising universality. We further extend the calculations of the chiral tricritical behaviors of Ising spins to the case of Heisenberg spins. The experimental relevance of the CTP in two-dimensional Dirac semimetals is also discussed.

Unsupervised machine learning account of magnetic transitions in the Hubbard model

NASA Astrophysics Data System (ADS)

Ch'ng, Kelvin; Vazquez, Nick; Khatami, Ehsan

2018-01-01

We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t -distributed stochastic neighboring ensemble (t -SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t -SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t -SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.

Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models

NASA Astrophysics Data System (ADS)

Steinhaus, Sebastian

2015-09-01

The universal coupling of matter and gravity is one of the most important features of general relativity. In quantum gravity, in particular spin foams, matter couplings have been defined in the past, yet the mutual dynamics, in particular if matter and gravity are strongly coupled, are hardly explored, which is related to the definition of both matter and gravitational degrees of freedom on the discretization. However, extracting these mutual dynamics is crucial in testing the viability of the spin foam approach and also establishing connections to other discrete approaches such as lattice gauge theories. Therefore, we introduce a simple two-dimensional toy model for Yang-Mills coupled to spin foams, namely an Ising model coupled to so-called intertwiner models defined for SU (2 )k. The two systems are coupled by choosing the Ising coupling constant to depend on spin labels of the background, as these are interpreted as the edge lengths of the discretization. We coarse grain this toy model via tensor network renormalization and uncover an interesting dynamics: the Ising phase transition temperature turns out to be sensitive to the background configurations and conversely, the Ising model can induce phase transitions in the background. Moreover, we observe a strong coupling of both systems if close to both phase transitions.

Aging in the three-dimensional random-field Ising model

NASA Astrophysics Data System (ADS)

von Ohr, Sebastian; Manssen, Markus; Hartmann, Alexander K.

2017-07-01

We studied the nonequilibrium aging behavior of the random-field Ising model in three dimensions for various values of the disorder strength. This allowed us to investigate how the aging behavior changes across the ferromagnetic-paramagnetic phase transition. We investigated a large system size of N =2563 spins and up to 108 Monte Carlo sweeps. To reach these necessary long simulation times, we employed an implementation running on Intel Xeon Phi coprocessors, reaching single-spin-flip times as short as 6 ps. We measured typical correlation functions in space and time to extract a growing length scale and corresponding exponents.

Localization in a random XY model with long-range interactions: Intermediate case between single-particle and many-body problems

NASA Astrophysics Data System (ADS)

Burin, Alexander L.

2015-09-01

Many-body localization in an XY model with a long-range interaction is investigated. We show that in the regime of a high strength of disordering compared to the interaction an off-resonant flip-flop spin-spin interaction (hopping) generates the effective Ising interactions of spins in the third order of perturbation theory in a hopping. The combination of hopping and induced Ising interactions for the power-law distance dependent hopping V (R ) ∝R-α always leads to the localization breakdown in a thermodynamic limit of an infinite system at α <3 d /2 where d is a system dimension. The delocalization takes place due to the induced Ising interactions U (R ) ∝R-2 α of "extended" resonant pairs. This prediction is consistent with the numerical finite size scaling in one-dimensional systems. Many-body localization in an XY model is more stable with respect to the long-range interaction compared to a many-body problem with similar Ising and Heisenberg interactions requiring α ≥2 d which makes the practical implementations of this model more attractive for quantum information applications. The full summary of dimension constraints and localization threshold size dependencies for many-body localization in the case of combined Ising and hopping interactions is obtained using this and previous work and it is the subject for the future experimental verification using cold atomic systems.

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.

PubMed

Wu, Jianda; Kormos, Márton; Si, Qimiao

2014-12-12

A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.

Quantum quench in an atomic one-dimensional Ising chain.

PubMed

Meinert, F; Mark, M J; Kirilov, E; Lauber, K; Weinmann, P; Daley, A J; Nägerl, H-C

2013-08-02

We study nonequilibrium dynamics for an ensemble of tilted one-dimensional atomic Bose-Hubbard chains after a sudden quench to the vicinity of the transition point of the Ising paramagnetic to antiferromagnetic quantum phase transition. The quench results in coherent oscillations for the orientation of effective Ising spins, detected via oscillations in the number of doubly occupied lattice sites. We characterize the quench by varying the system parameters. We report significant modification of the tunneling rate induced by interactions and show clear evidence for collective effects in the oscillatory response.

Comparison of the ferromagnetic Blume-Emery-Griffiths model and the AF spin-1 longitudinal Ising model at low temperature

NASA Astrophysics Data System (ADS)

Thomaz, M. T.; Corrêa Silva, E. V.

2016-03-01

We derive the exact Helmholtz free energy (HFE) of the standard and staggered one-dimensional Blume-Emery-Griffiths (BEG) model in the presence of an external longitudinal magnetic field. We discuss in detail the thermodynamic behavior of the ferromagnetic version of the model, which exhibits magnetic field-dependent plateaux in the z-component of its magnetization at low temperatures. We also study the behavior of its specific heat and entropy, both per site, at finite temperature. The degeneracy of the ground state, at T=0, along the lines that separate distinct phases in the phase diagram of the ferromagnetic BEG model is calculated, extending the study of the phase diagram of the spin-1 antiferromagnetic (AF) Ising model in S.M. de Souza and M.T. Thomaz, J. Magn. and Magn. Mater. 354 (2014) 205 [5]. We explore the implications of the equality of phase diagrams, at T=0, of the ferromagnetic BEG model with K/|J| = - 2 and of the spin-1 AF Ising model for D/|J| > 1/2.

Rotational Invariance of the 2d Spin - Spin Correlation Function

NASA Astrophysics Data System (ADS)

Pinson, Haru

2012-09-01

At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3-5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22-26, 1984, JINR, vol II, pp 138-151, 1985).

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE PAGES

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

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

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

NASA Astrophysics Data System (ADS)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.

2018-04-01

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1  +  1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

New developments in the theoretical treatment of low dimensional strongly correlated systems.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M

2017-10-09

We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1  +  1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model

NASA Astrophysics Data System (ADS)

Kassebaum, Paul G.; Iannacchione, Germano S.

The fundamental nature of an evolving one-dimensional (1D) Ising model is investigated with an elementary cellular automaton (CA) simulation. The emergent CA simulation employs an ensemble of cells in one spatial dimension, each cell capable of two microstates interacting with simple nearest-neighbor rules and incorporating an external field. The behavior of the CA model provides insight into the dynamics of coupled two-state systems not expressible by exact analytical solutions. For instance, state progression graphs show the causal dynamics of a system through time in relation to the system's entropy. Unique graphical analysis techniques are introduced through difference patterns, diffusion patterns, and state progression graphs of the 1D ensemble visualizing the evolution. All analyses are consistent with the known behavior of the 1D Ising system. The CA simulation and new pattern recognition techniques are scalable (in both dimension, complexity, and size) and have many potential applications such as complex design of materials, control of agent systems, and evolutionary mechanism design.

On the quantum symmetry of the chiral Ising model

NASA Astrophysics Data System (ADS)

Vecsernyés, Peter

1994-03-01

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.

Effect of antifreeze protein on heterogeneous ice nucleation based on a two-dimensional random-field Ising model

NASA Astrophysics Data System (ADS)

Dong, Zhen; Wang, Jianjun; Zhou, Xin

2017-05-01

Antifreeze proteins (AFPs) are the key biomolecules that protect many species from suffering the extreme conditions. Their unique properties of antifreezing provide the potential of a wide range of applications. Inspired by the present experimental approaches of creating an antifreeze surface by coating AFPs, here we present a two-dimensional random-field lattice Ising model to study the effect of AFPs on heterogeneous ice nucleation. The model shows that both the size and the free-energy effect of individual AFPs and their surface coverage dominate the antifreeze capacity of an AFP-coated surface. The simulation results are consistent with the recent experiments qualitatively, revealing the origin of the surprisingly low antifreeze capacity of an AFP-coated surface when the coverage is not particularly high as shown in experiment. These results will hopefully deepen our understanding of the antifreeze effects and thus be potentially useful for designing novel antifreeze coating materials based on biomolecules.

Rise of pairwise thermal entanglement for an alternating Ising and Heisenberg spin chain in an arbitrarily oriented magnetic field

NASA Astrophysics Data System (ADS)

Rojas, M.; de Souza, S. M.; Rojas, Onofre

2014-03-01

Typically two particles (spins) could be maximally entangled at zero temperature, and for a certain temperature the phenomenon of entanglement vanishes at the threshold temperature. For the Heisenberg coupled model or even the Ising model with a transverse magnetic field, one can observe some rise of entanglement even for a disentangled region at zero temperature. So we can understand this emergence of entanglement at finite temperature as being due to the mixing of some maximally entangled states with some other untangled states. Here, we present a simple one-dimensional Ising model with alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field, which can be mapped onto the classical Ising model with a magnetic field. This model does not show any evidence of entanglement at zero temperature, but surprisingly at finite temperature rise a pairwise thermal entanglement between two untangled spins at zero temperature when an arbitrarily oriented magnetic field is applied. This effect is a purely magnetic field, and the temperature dependence, as soon as the temperature increases, causes a small increase in concurrence, achieving its maximum at around 0.1. Even for long-range entanglement, a weak concurrence still survives. There are also some real materials that could serve as candidates that would exhibit this effect, such as Dy(NO3)(DMSO)2Cu(opba)(DMSO)2 [DMSO = dimethyl sulfoxide; opba = o-phenylenebis(oxamoto)] [J. Strečka, M. Hagiwara, Y. Han, T. Kida, Z. Honda, and M. Ikeda, Condens. Matter Phys. 15, 43002 (2012), 10.5488/CMP.15.43002].

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator.

PubMed

Farajollahpour, T; Jafari, S A

2018-01-10

We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the 'ARPES-dark' state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.

Semiconductor of spinons: from Ising band insulator to orthogonal band insulator

NASA Astrophysics Data System (ADS)

Farajollahpour, T.; Jafari, S. A.

2018-01-01

We use the ionic Hubbard model to study the effects of strong correlations on a two-dimensional semiconductor. The spectral gap in the limit where on-site interactions are zero is set by the staggered ionic potential, while in the strong interaction limit it is set by the Hubbard U. Combining mean field solutions of the slave spin and slave rotor methods, we propose two interesting gapped phases in between: (i) the insulating phase before the Mott phase can be viewed as gapping a non-Fermi liquid state of spinons by the staggered ionic potential. The quasi-particles of underlying spinons are orthogonal to physical electrons, giving rise to the ‘ARPES-dark’ state where the ARPES gap will be larger than the optical and thermal gap. (ii) The Ising insulator corresponding to ordered phase of the Ising variable is characterized by single-particle excitations whose dispersion is controlled by Ising-like temperature and field dependences. The temperature can be conveniently employed to drive a phase transition between these two insulating phases where Ising exponents become measurable by ARPES and cyclotron resonance. The rare earth monochalcogenide semiconductors where the magneto-resistance is anomalously large can be a candidate system for the Ising band insulator. We argue that the Ising and orthogonal insulating phases require strong enough ionic potential to survive the downward renormalization of the ionic potential caused by Hubbard U.

Emergent Ising degrees of freedom above a double-stripe magnetic ground state [Emergent Ising degrees of freedom above double-stripe magnetism

DOE PAGES

Zhang, Guanghua; Flint, Rebecca

2017-12-27

Here, double-stripe magnetism [Q=(π/2,π/2)] has been proposed as the magnetic ground state for both the iron-telluride and BaTi 2Sb 2O families of superconductors. Double-stripe order is captured within a J 1–J 2–J 3 Heisenberg model in the regime J 3 >> J 2 >> J 1. Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π,π). Because the ground state is fourfold degenerate, modulo rotations in spin space,more » only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.« less

Emergent Ising degrees of freedom above a double-stripe magnetic ground state [Emergent Ising degrees of freedom above double-stripe magnetism

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

Zhang, Guanghua; Flint, Rebecca

Here, double-stripe magnetism [Q=(π/2,π/2)] has been proposed as the magnetic ground state for both the iron-telluride and BaTi 2Sb 2O families of superconductors. Double-stripe order is captured within a J 1–J 2–J 3 Heisenberg model in the regime J 3 >> J 2 >> J 1. Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π,π). Because the ground state is fourfold degenerate, modulo rotations in spin space,more » only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.« less

Emergent Ising degrees of freedom above a double-stripe magnetic ground state

NASA Astrophysics Data System (ADS)

Zhang, Guanghua; Flint, Rebecca

2017-12-01

Double-stripe magnetism [Q =(π /2 ,π /2 )] has been proposed as the magnetic ground state for both the iron-telluride and BaTi2Sb2O families of superconductors. Double-stripe order is captured within a J1-J2-J3 Heisenberg model in the regime J3≫J2≫J1 . Intriguingly, besides breaking spin-rotational symmetry, the ground-state manifold has three additional Ising degrees of freedom associated with bond ordering. Via their coupling to the lattice, they give rise to an orthorhombic distortion and to two nonuniform lattice distortions with wave vector (π ,π ) . Because the ground state is fourfold degenerate, modulo rotations in spin space, only two of these Ising bond order parameters are independent. Here, we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order, and solve it within a large-N limit. All three transitions, corresponding to the condensations of two Ising bond order parameters and one magnetic order parameter are simultaneous and first order in three dimensions, but lower dimensionality, or equivalently weaker interlayer coupling, and weaker magnetoelastic coupling can split the three transitions, and in some cases allows for two separate Ising phase transitions above the magnetic one.

Multipoint Green's functions in 1 + 1 dimensional integrable quantum field theories

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2017-02-14

We calculate the multipoint Green functions in 1+1 dimensional integrable quantum field theories. We use the crossing formula for general models and calculate the 3 and 4 point functions taking in to account only the lower nontrivial intermediate states contributions. Then we apply the general results to the examples of the scaling Z 2 Ising model, sinh-Gordon model and Z 3 scaling Potts model. We demonstrate this calculations explicitly. The results can be applied to physical phenomena as for example to the Raman scattering.

Deep neural networks for direct, featureless learning through observation: The case of two-dimensional spin models

NASA Astrophysics Data System (ADS)

Mills, Kyle; Tamblyn, Isaac

2018-03-01

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4 ×4 Ising model. Using its success at this task, we motivate the study of the larger 8 ×8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration.

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Kim, Kyungsik; Lee, Dong-In; Scalas, Enrico

2008-05-01

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

Absence of long range order in SrDy2O4 frustrated magnet due to trapped defects from a dimensionality crossover

NASA Astrophysics Data System (ADS)

Gauthier, Nicolas; Fennell, Amy; Uldry, Anne-Christine; Delley, Bernard; Sibille, Romain; White, Jonathan; Niedermayer, Christof; Pomjakushin, Vladimir; Kenzelmann, Michel; Prevost, Bobby; Desilets-Benoit, Alexandre; Bianchi, Andrea D.; Dabkowska, Hanna A.; Nilsen, Goran; Regnault, Louis-Pierre

The simultaneous occurence of geometrical frustration and low dimensionality can lead to strongly correlated fluctuating ground states. In the SrLn2O4 compounds, the Ln magnetic ions form one-dimensional (1D) zig-zag chains that have both of these characteristics, offering a playground to study novel states of matter. In SrDy2O4, the two inequivalent Dy3+ sites are Ising-like with perpendicular easy-axes, favouring the decoupling of neighbouring zig-zag chains. No long range order is observed down to T = 60 mK in zero field but diffuse neutron scattering indicates short range correlations that are consistent with those of the 1D Ising zig-zag chain model. AC susceptibility measurements indicate a slowing down of the fluctuations at low temperatures. We attribute this behaviour to the domain walls in the zig-zag chains. Experimental evidence of a dimensionality crossover at low temperatures in SrDy2O4 suggest that the domains walls are trapped because of interchain interactions, precluding long-range order to the lowest temperatures.

Effect of External Economic-Field Cycle and Market Temperature on Stock-Price Hysteresis: Monte Carlo Simulation on the Ising Spin Model

NASA Astrophysics Data System (ADS)

Punya Jaroenjittichai, Atchara; Laosiritaworn, Yongyut

2017-09-01

In this work, the stock-price versus economic-field hysteresis was investigated. The Ising spin Hamiltonian was utilized as the level of ‘disagreement’ in describing investors’ behaviour. The Ising spin directions were referred to an investor’s intention to perform his action on trading his stock. The periodic economic variation was also considered via the external economic-field in the Ising model. The stochastic Monte Carlo simulation was performed on Ising spins, where the steady-state excess demand and supply as well as the stock-price were extracted via the magnetization. From the results, the economic-field parameters and market temperature were found to have significant effect on the dynamic magnetization and stock-price behaviour. Specifically, the hysteresis changes from asymmetric to symmetric loops with increasing market temperature and economic-field strength. However, the hysteresis changes from symmetric to asymmetric loops with increasing the economic-field frequency, when either temperature or economic-field strength is large enough, and returns to symmetric shape at very high frequencies. This suggests competitive effects among field and temperature factors on the hysteresis characteristic, implying multi-dimensional complicated non-trivial relationship among inputs-outputs. As is seen, the results reported (over extensive range) can be used as basis/guideline for further analysis/quantifying how economic-field and market-temperature affect the stock-price distribution on the course of economic cycle.

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).

Inverse Ising Inference Using All the Data

NASA Astrophysics Data System (ADS)

Aurell, Erik; Ekeberg, Magnus

2012-03-01

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

Quantum transitions driven by one-bond defects in quantum Ising rings.

PubMed

Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore

2015-04-01

We investigate quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models. We consider quantum Ising rings in the presence of a bond defect. In the ordered phase, the system undergoes a quantum transition driven by the bond defect between a magnet phase, in which the gap decreases exponentially with increasing size, and a kink phase, in which the gap decreases instead with a power of the size. Close to the transition, the system shows a universal scaling behavior, which we characterize by computing, either analytically or numerically, scaling functions for the low-level energy differences and the two-point correlation function. We discuss the implications of these results for the nonequilibrium dynamics in the presence of a slowly varying parallel magnetic field h, when going across the first-order quantum transition at h=0.

Three-dimensional analytical model for the spatial variation of the foreshock electron distribution function - Systematics and comparisons with ISEE observations

NASA Technical Reports Server (NTRS)

Fitzenreiter, R. J.; Scudder, J. D.; Klimas, A. J.

1990-01-01

A model which is consistent with the solar wind and shock surface boundary conditions for the foreshock electron distribution in the absence of wave-particle effects is formulated for an arbitrary location behind the magnetic tangent to the earth's bow shock. Variations of the gyrophase-averaged velocity distribution are compared and contrasted with in situ ISEE observations. It is found that magnetic mirroring of solar wind electrons is the most important process by which nonmonotonic reduced electron distributions in the foreshock are produced. Leakage of particles from the magnetosheath is shown to be relatively unimportant in determining reduced distributions that are nonmonotonic. The two-dimensional distribution function off the magnetic field direction is the crucial contribution in producing reduced distributions which have beams. The time scale for modification of the electron velocity distribution in velocity space can be significantly influenced by steady state spatial gradients in the background imposed by the curved shock geometry.

Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios

NASA Astrophysics Data System (ADS)

Hobrecht, Hendrik; Hucht, Alfred

2017-02-01

We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representation of the corresponding partition function Z on an L× M square lattice, wrapped around a torus with aspect ratio ρ =L/M . By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a 2× 2 transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films ρ \\to 0 . Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.

Ising tricriticality in the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

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

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results. This work was supported by Deutsche Forschungsgemeinschaft (Germany), SFB 652, project B5, and by the EPSRC under Grant No. EP/N01930X/1 (FHLE).

Testing ground for fluctuation theorems: The one-dimensional Ising model

NASA Astrophysics Data System (ADS)

Lemos, C. G. O.; Santos, M.; Ferreira, A. L.; Figueiredo, W.

2018-04-01

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Critical scaling of the mutual information in two-dimensional disordered Ising models

NASA Astrophysics Data System (ADS)

Sriluckshmy, P. V.; Mandal, Ipsita

2018-04-01

Rényi mutual information, computed from second Rényi entropies, can identify classical phase transitions from their finite-size scaling at critical points. We apply this technique to examine the presence or absence of finite temperature phase transitions in various two-dimensional models on a square lattice, which are extensions of the conventional Ising model by adding a quenched disorder. When the quenched disorder causes the nearest neighbor bonds to be both ferromagnetic and antiferromagnetic, (a) a spin glass phase exists only at zero temperature, and (b) a ferromagnetic phase exists at a finite temperature when the antiferromagnetic bond distributions are sufficiently dilute. Furthermore, finite temperature paramagnetic-ferromagnetic transitions can also occur when the disordered bonds involve only ferromagnetic couplings of random strengths. In our numerical simulations, the ‘zero temperature only’ phase transitions are identified when there is no consistent finite-size scaling of the Rényi mutual information curves, while for finite temperature critical points, the curves can identify the critical temperature T c by their crossings at T c and 2 Tc .

Test of quantum thermalization in the two-dimensional transverse-field Ising model

PubMed Central

Blaß, Benjamin; Rieger, Heiko

2016-01-01

We study the quantum relaxation of the two-dimensional transverse-field Ising model after global quenches with a real-time variational Monte Carlo method and address the question whether this non-integrable, two-dimensional system thermalizes or not. We consider both interaction quenches in the paramagnetic phase and field quenches in the ferromagnetic phase and compare the time-averaged probability distributions of non-conserved quantities like magnetization and correlation functions to the thermal distributions according to the canonical Gibbs ensemble obtained with quantum Monte Carlo simulations at temperatures defined by the excess energy in the system. We find that the occurrence of thermalization crucially depends on the quench parameters: While after the interaction quenches in the paramagnetic phase thermalization can be observed, our results for the field quenches in the ferromagnetic phase show clear deviations from the thermal system. These deviations increase with the quench strength and become especially clear comparing the shape of the thermal and the time-averaged distributions, the latter ones indicating that the system does not completely lose the memory of its initial state even for strong quenches. We discuss our results with respect to a recently formulated theorem on generalized thermalization in quantum systems. PMID:27905523

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit.

PubMed

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén; Klein, Dahlia R; Cheng, Ran; Seyler, Kyle L; Zhong, Ding; Schmidgall, Emma; McGuire, Michael A; Cobden, David H; Yao, Wang; Xiao, Di; Jarillo-Herrero, Pablo; Xu, Xiaodong

2017-06-07

Since the discovery of graphene, the family of two-dimensional materials has grown, displaying a broad range of electronic properties. Recent additions include semiconductors with spin-valley coupling, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semimetals with edge transport. However, no two-dimensional crystal with intrinsic magnetism has yet been discovered; such a crystal would be useful in many technologies from sensing to data storage. Theoretically, magnetic order is prohibited in the two-dimensional isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. Magnetic anisotropy removes this restriction, however, and enables, for instance, the occurrence of two-dimensional Ising ferromagnetism. Here we use magneto-optical Kerr effect microscopy to demonstrate that monolayer chromium triiodide (CrI 3 ) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 kelvin is only slightly lower than that of the bulk crystal, 61 kelvin, which is consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phase, highlighting thickness-dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI 3 displays suppressed magnetization with a metamagnetic effect, whereas in trilayer CrI 3 the interlayer ferromagnetism observed in the bulk crystal is restored. This work creates opportunities for studying magnetism by harnessing the unusual features of atomically thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering to produce interface phenomena.

Transverse spin correlations of the random transverse-field Ising model

NASA Astrophysics Data System (ADS)

Iglói, Ferenc; Kovács, István A.

2018-03-01

The critical behavior of the random transverse-field Ising model in finite-dimensional lattices is governed by infinite disorder fixed points, several properties of which have already been calculated by the use of the strong disorder renormalization-group (SDRG) method. Here we extend these studies and calculate the connected transverse-spin correlation function by a numerical implementation of the SDRG method in d =1 ,2 , and 3 dimensions. At the critical point an algebraic decay of the form ˜r-ηt is found, with a decay exponent being approximately ηt≈2 +2 d . In d =1 the results are related to dimer-dimer correlations in the random antiferromagnetic X X chain and have been tested by numerical calculations using free-fermionic techniques.

Frozen into stripes: fate of the critical Ising model after a quench.

PubMed

Blanchard, T; Picco, M

2013-09-01

In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

Deep Neural Network Detects Quantum Phase Transition

NASA Astrophysics Data System (ADS)

Arai, Shunta; Ohzeki, Masayuki; Tanaka, Kazuyuki

2018-03-01

We detect the quantum phase transition of a quantum many-body system by mapping the observed results of the quantum state onto a neural network. In the present study, we utilized the simplest case of a quantum many-body system, namely a one-dimensional chain of Ising spins with the transverse Ising model. We prepared several spin configurations, which were obtained using repeated observations of the model for a particular strength of the transverse field, as input data for the neural network. Although the proposed method can be employed using experimental observations of quantum many-body systems, we tested our technique with spin configurations generated by a quantum Monte Carlo simulation without initial relaxation. The neural network successfully identified the strength of transverse field only from the spin configurations, leading to consistent estimations of the critical point of our model Γc = J.

Realization of the axial next-nearest-neighbor Ising model in U 3 Al 2 Ge 3

DOE PAGES

Fobes, David M.; Lin, Shi-Zeng; Ghimire, Nirmal J.; ...

2017-11-09

Inmore » this paper, we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U 3 Al 2 Ge 3 . Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order at T N = 63 K to be second order and a first-order phase transition to ferromagnetic order at T c = 48 K. Within the sinusoidally modulated magnetic phase (T c < T < T N), we uncover a dramatic change, by a factor of 3, in the ordering wave vector as a function of temperature. Finally, these observations all indicate that U 3 Al 2 Ge 3 is a close realization of the three-dimensional axial next-nearest-neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.« less

Realization of the axial next-nearest-neighbor Ising model in U 3 Al 2 Ge 3

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

Fobes, David M.; Lin, Shi-Zeng; Ghimire, Nirmal J.

Inmore » this paper, we report small-angle neutron scattering (SANS) measurements and theoretical modeling of U 3 Al 2 Ge 3 . Analysis of the SANS data reveals a phase transition to sinusoidally modulated magnetic order at T N = 63 K to be second order and a first-order phase transition to ferromagnetic order at T c = 48 K. Within the sinusoidally modulated magnetic phase (T c < T < T N), we uncover a dramatic change, by a factor of 3, in the ordering wave vector as a function of temperature. Finally, these observations all indicate that U 3 Al 2 Ge 3 is a close realization of the three-dimensional axial next-nearest-neighbor Ising model, a prototypical framework for describing commensurate to incommensurate phase transitions in frustrated magnets.« less

CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2014-03-01

We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K.A. Hawick, A. Leist, and D. P. Playne, Parallel Computing 36 (2010) 655-678 [2] O. Kalentev, A. Rai, S. Kemnitzb, and R. Schneider, J. Parallel Distrib. Comput. 71 (2011) 615-620

Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

PubMed

Vahedi, J; Ashouri, A; Mahdavifar, S

2016-10-01

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

Multipartite entanglement characterization of a quantum phase transition

NASA Astrophysics Data System (ADS)

Costantini, G.; Facchi, P.; Florio, G.; Pascazio, S.

2007-07-01

A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.

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.

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

Barber, M.N.; Derrida, B.

We study the phase diagram of the two-dimensional anisotropic next-nearest neighbor Ising (ANNNI) model by comparing the time evolution of two distinct spin configurations submitted to the same thermal noise. We clearly se several dynamical transitions between ferromagnetic, paramagnetic, antiphase, and floating phases. These dynamical transitions seem to occur rather close to the transition lines determined previously in the literature.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion.

PubMed

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Nonequilibrium two-dimensional Ising model with stationary uphill diffusion

NASA Astrophysics Data System (ADS)

Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia

2018-03-01

Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.

Mixed-order phase transition in a one-dimensional model.

PubMed

Bar, Amir; Mukamel, David

2014-01-10

We introduce and analyze an exactly soluble one-dimensional Ising model with long range interactions that exhibits a mixed-order transition, namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models that are seemingly unrelated. The model we present serves as a link between two classes of models that exhibit a mixed-order transition in one dimension, namely, spin models with a coupling constant that decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.

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

NASA Astrophysics Data System (ADS)

Maksymov, Andrii O.; Rahman, Noah; Kapit, Eliot; Burin, Alexander L.

2017-11-01

This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r-α, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015), 10.1103/PhysRevB.91.094202] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for α ≤2 d in a d -dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 ≤α ≤d . The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)10.1103/PhysRevA.94.063625].

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study.

PubMed

Singh, R R P; Young, A P

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d -dimensional hypercubic lattices: A series expansion study

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-08-01

We study the ±J transverse-field Ising spin-glass model at zero temperature on d -dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d =6 , which is below the upper critical dimension of d =8 . In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

Gaps between avalanches in one-dimensional random-field Ising models

NASA Astrophysics Data System (ADS)

Nampoothiri, Jishnu N.; Ramola, Kabir; Sabhapandit, Sanjib; Chakraborty, Bulbul

2017-09-01

We analyze the statistics of gaps (Δ H ) between successive avalanches in one-dimensional random-field Ising models (RFIMs) in an external field H at zero temperature. In the first part of the paper we study the nearest-neighbor ferromagnetic RFIM. We map the sequence of avalanches in this system to a nonhomogeneous Poisson process with an H -dependent rate ρ (H ) . We use this to analytically compute the distribution of gaps P (Δ H ) between avalanches as the field is increased monotonically from -∞ to +∞ . We show that P (Δ H ) tends to a constant C (R ) as Δ H →0+ , which displays a nontrivial behavior with the strength of disorder R . We verify our predictions with numerical simulations. In the second part of the paper, motivated by avalanche gap distributions in driven disordered amorphous solids, we study a long-range antiferromagnetic RFIM. This model displays a gapped behavior P (Δ H )=0 up to a system size dependent offset value Δ Hoff , and P (Δ H ) ˜(ΔH -Δ Hoff) θ as Δ H →Hoff+ . We perform numerical simulations on this model and determine θ ≈0.95 (5 ) . We also discuss mechanisms which would lead to a nonzero exponent θ for general spin models with quenched random fields.

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

An Experimental Study of the Ising Chain Statistics under the Magnetic Field

NASA Astrophysics Data System (ADS)

Takeda, Kazuyoshi; Wada, Masaru

1981-11-01

The first experimental study of the statistics of a quasi-one-dimensional Ising system under the magnetic field Hα, described by the Hamiltonian \\includegraphics{dummy.eps} has been performed, where J1 and J2 are the intra- and the inter-chain exchange constants, respectively. A single crystal of the compound (CH3)3NHCoCl3\\cdot2H2O has been used as a model sample of the ferromagnetic system with J1/kB{=}14.2 K and J2/kB{=}0.20 K. It has been revealed that the experimental values of the magnetic heat capacity under the field Hα>2J2/gzμB (≈0.8 kOe) applied along the spin preferential axis are excellently reproduced by the values calculated for the isolated Ising chain under the longitudinal field (α{=}z; gz{=}6.54). For the temperature higher than 7 K (≈J1/2kB), the experimental values of the magnetic heat capacity under the field along the spin hard axis have also agreed with the theoretical values for the isolated Ising chain under the transverse field (α{=}y; gy{=}3.90).

Microscopic image processing systems for measuring nonuniform film thickness profiles

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

Liu, A.H.; Plawsky, J.L.; DasGupta, S.

1994-01-01

In very thin liquid films. transport processes are controlled by the temperature and the interfacial intermolecular force field which is a function of the film thickness profile and interfacial properties. The film thickness profile and interfacial properties can be measured most efficiently using a microscopic image processing system. IPS, to record the intensity pattern of the reflected light from the film. There are two types of IPS: an image analyzing interferometer (IAI) and/or an image scanning ellipsometer (ISE). The ISE is a novel technique to measure the two dimensional thickness profile of a nonuniform, thin film, from 1 nm upmore » to several {mu}m, in a steady state as well as in a transient state. It is a full field imaging technique which can study every point on the surface simultaneously with high spatial resolution and thickness sensitivity, i.e., it can measure and map the 2-D film thickness profile. Using the ISE, the transient thickness profile of a draining thin liquid film was measured and modeled. The interfacial conditions were determined in situ by measuring the Hamaker constant. The ISE and IAI systems are compared.« less

Dynamical transitions of a driven Ising interface

NASA Astrophysics Data System (ADS)

Sahai, Manish K.; Sengupta, Surajit

2008-03-01

We study the structure of an interface in a three-dimensional Ising system created by an external nonuniform field H(r,t) . H changes sign over a two-dimensional plane of arbitrary orientation. When the field is pulled with velocity ve , [i.e., H(r,t)=H(r-vet) ], the interface undergoes several dynamical transitions. For low velocities it is pinned by the field profile and moves along with it, the distribution of local slopes undergoing a series of commensurate-incommensurate transitions. For large ve the interface depins and grows with Kardar-Parisi-Zhang exponents.

Nature versus nurture: Predictability in low-temperature Ising dynamics

NASA Astrophysics Data System (ADS)

Ye, J.; Machta, J.; Newman, C. M.; Stein, D. L.

2013-10-01

Consider a dynamical many-body system with a random initial state subsequently evolving through stochastic dynamics. What is the relative importance of the initial state (“nature”) versus the realization of the stochastic dynamics (“nurture”) in predicting the final state? We examined this question for the two-dimensional Ising ferromagnet following an initial deep quench from T=∞ to T=0. We performed Monte Carlo studies on the overlap between “identical twins” raised in independent dynamical environments, up to size L=500. Our results suggest an overlap decaying with time as t-θh with θh=0.22±0.02; the same exponent holds for a quench to low but nonzero temperature. This “heritability exponent” may equal the persistence exponent for the two-dimensional Ising ferromagnet, but the two differ more generally.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions

NASA Technical Reports Server (NTRS)

Rice, John Jeremy; Stolovitzky, Gustavo; Tu, Yuhai; de Tombe, Pieter P.; Bers, D. M. (Principal Investigator)

2003-01-01

We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa (F-pCa) relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point (Ca(50)) compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the F-pCa relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near Ca(50), and becomes uncooperative again at higher [Ca]. The steepness near Ca(50) mirrors the steep F-pCa as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near Ca(50), high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of F-pCa relations that other models fail to reproduce.

RG flow from Φ 4 theory to the 2D Ising model

DOE PAGES

Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel; ...

2017-08-16

We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along themore » full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.« less

Thermodynamics of alternating spin chains with competing nearest- and next-nearest-neighbor interactions: Ising model

NASA Astrophysics Data System (ADS)

Pini, Maria Gloria; Rettori, Angelo

1993-08-01

The thermodynamical properties of an alternating spin (S,s) one-dimensional (1D) Ising model with competing nearest- and next-nearest-neighbor interactions are exactly calculated using a transfer-matrix technique. In contrast to the case S=s=1/2, previously investigated by Harada, the alternation of different spins (S≠s) along the chain is found to give rise to two-peaked static structure factors, signaling the coexistence of different short-range-order configurations. The relevance of our calculations with regard to recent experimental data by Gatteschi et al. in quasi-1D molecular magnetic materials, R (hfac)3 NITEt (R=Gd, Tb, Dy, Ho, Er, . . .), is discussed; hfac is hexafluoro-acetylacetonate and NlTEt is 2-Ethyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxyl-3-oxide.

Magnetic and thermodynamic properties of Ising model with borophene structure in a longitudinal magnetic field

NASA Astrophysics Data System (ADS)

Shi, Kaile; Jiang, Wei; Guo, Anbang; Wang, Kai; Wu, Chuang

2018-06-01

The magnetic and thermodynamic properties of borophene structure have been studied for the first time by Monte Carlo simulation. Two-dimensional borophene structure consisting of seven hexagonal B36 units is described by Ising model. Each B36 basic unit includes three benzene-like with spin-3/2. The general formula for the borophene structure is given. The numerical results of the magnetization, the magnetic susceptibility, the internal energy and the specific heat are studied with various parameters. The possibility to test the predicted magnetism in experiment are illustrated, for instance, the maximum on the magnetization curve. The multiple hysteresis loops and the magnetization plateaus are sensitive to the ferromagnetic or ferrimagnetic exchange coupling in borophene structure. The results show the borophene structure could have applications in spintronics, which deserves further studies in experiments.

Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

Correction to verdonck and tuerlinckx (2014).

PubMed

2015-01-01

Reports an error in "The Ising Decision Maker: A binary stochastic network for choice response time" by Stijn Verdonck and Francis Tuerlinckx (Psychological Review, 2014[Jul], Vol 121[3], 422-462). An inaccurate assumption in Appendix B (provided in the erratum) led to an oversimplified result in Equation 18 (the diffusion equations associated with the microscopically defined dynamics). The authors sincerely thank Rani Moran for making them aware of the problem. Only the expression of the diffusion coefficient D is incorrect, and should be changed, as indicated in the erratum. Both the cause of the problem and the solution are also explained in the erratum. (The following abstract of the original article appeared in record 2014-31650-006.) The Ising Decision Maker (IDM) is a new formal model for speeded two-choice decision making derived from the stochastic Hopfield network or dynamic Ising model. On a microscopic level, it consists of 2 pools of binary stochastic neurons with pairwise interactions. Inside each pool, neurons excite each other, whereas between pools, neurons inhibit each other. The perceptual input is represented by an external excitatory field. Using methods from statistical mechanics, the high-dimensional network of neurons (microscopic level) is reduced to a two-dimensional stochastic process, describing the evolution of the mean neural activity per pool (macroscopic level). The IDM can be seen as an abstract, analytically tractable multiple attractor network model of information accumulation. In this article, the properties of the IDM are studied, the relations to existing models are discussed, and it is shown that the most important basic aspects of two-choice response time data can be reproduced. In addition, the IDM is shown to predict a variety of observed psychophysical relations such as Piéron's law, the van der Molen-Keuss effect, and Weber's law. Using Bayesian methods, the model is fitted to both simulated and real data, and its performance is compared to the Ratcliff diffusion model. (PsycINFO Database Record (c) 2015 APA, all rights reserved).

Order by disorder and gaugelike degeneracy in a quantum pyrochlore antiferromagnet.

PubMed

Henley, Christopher L

2006-02-03

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic-order) spin-wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z2 lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L3). All these ground states have unit cells bigger than those considered previously.

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.

Linking market interaction intensity of 3D Ising type financial model with market volatility

NASA Astrophysics Data System (ADS)

Fang, Wen; Ke, Jinchuan; Wang, Jun; Feng, Ling

2016-11-01

Microscopic interaction models in physics have been used to investigate the complex phenomena of economic systems. The simple interactions involved can lead to complex behaviors and help the understanding of mechanisms in the financial market at a systemic level. This article aims to develop a financial time series model through 3D (three-dimensional) Ising dynamic system which is widely used as an interacting spins model to explain the ferromagnetism in physics. Through Monte Carlo simulations of the financial model and numerical analysis for both the simulation return time series and historical return data of Hushen 300 (HS300) index in Chinese stock market, we show that despite its simplicity, this model displays stylized facts similar to that seen in real financial market. We demonstrate a possible underlying link between volatility fluctuations of real stock market and the change in interaction strengths of market participants in the financial model. In particular, our stochastic interaction strength in our model demonstrates that the real market may be consistently operating near the critical point of the system.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

Identifying differentially expressed genes in cancer patients using a non-parameter Ising model.

PubMed

Li, Xumeng; Feltus, Frank A; Sun, Xiaoqian; Wang, James Z; Luo, Feng

2011-10-01

Identification of genes and pathways involved in diseases and physiological conditions is a major task in systems biology. In this study, we developed a novel non-parameter Ising model to integrate protein-protein interaction network and microarray data for identifying differentially expressed (DE) genes. We also proposed a simulated annealing algorithm to find the optimal configuration of the Ising model. The Ising model was applied to two breast cancer microarray data sets. The results showed that more cancer-related DE sub-networks and genes were identified by the Ising model than those by the Markov random field model. Furthermore, cross-validation experiments showed that DE genes identified by Ising model can improve classification performance compared with DE genes identified by Markov random field model. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bifurcation analysis and phase diagram of a spin-string model with buckled states.

PubMed

Ruiz-Garcia, M; Bonilla, L L; Prados, A

2017-12-01

We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.

Bifurcation analysis and phase diagram of a spin-string model with buckled states

NASA Astrophysics Data System (ADS)

Ruiz-Garcia, M.; Bonilla, L. L.; Prados, A.

2017-12-01

We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.

Entanglement in the Anisotropic Kondo Necklace Model

NASA Astrophysics Data System (ADS)

Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14

PubMed Central

Paddison, Joseph A. M.; Ong, Harapan S.; Hamp, James O.; Mukherjee, Paromita; Bai, Xiaojian; Tucker, Matthew G.; Butch, Nicholas P.; Castelnovo, Claudio; Mourigal, Martin; Dutton, S. E.

2016-01-01

The Ising model—in which degrees of freedom (spins) are binary valued (up/down)—is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration. PMID:27996012

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

PubMed

Inglis, Stephen; Melko, Roger G

2013-01-01

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Anisotropic dielectric properties of two-dimensional matrix in pseudo-spin ferroelectric system

NASA Astrophysics Data System (ADS)

Kim, Se-Hun

2016-10-01

The anisotropic dielectric properties of a two-dimensional (2D) ferroelectric system were studied using the statistical calculation of the pseudo-spin Ising Hamiltonian model. It is necessary to delay the time for measurements of the observable and the independence of the new spin configuration under Monte Carlo sampling, in which the thermal equilibrium state depends on the temperature and size of the system. The autocorrelation time constants of the normalized relaxation function were determined by taking temperature and 2D lattice size into account. We discuss the dielectric constants of a two-dimensional ferroelectric system by using the Metropolis method in view of the Slater-Takagi defect energies.

Self-dual random-plaquette gauge model and the quantum toric code

NASA Astrophysics Data System (ADS)

Takeda, Koujin; Nishimori, Hidetoshi

2004-05-01

We study the four-dimensional Z2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two-dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, pc=0.889972…, and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

Quantum transverse-field Ising model on an infinite tree from matrix product states

NASA Astrophysics Data System (ADS)

Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter; Sylvester, Igor

2008-06-01

We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.

The magnetisation distribution of the Ising model - a new approach

NASA Astrophysics Data System (ADS)

Hakan Lundow, Per; Rosengren, Anders

2010-03-01

A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ a generalisation of the binomial coefficients to describe the magnetisation distributions of the Ising model. For the complete graph this distribution is exact. For simple lattices of dimensions d=1 and d=5 the magnetisation distributions are remarkably well-fitted by the generalized binomial distributions. For d=4 we are only slightly less successful, while for d=2,3 we see some deviations (with exceptions!) between the generalized binomial and the Ising distribution. The results speak in favour of the generalized binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. A theoretical analysis of the distribution's moments also lends support their being correct asymptotically, including the logarithmic corrections in d=4. The full extent to which they correctly model the Ising distribution, and for which graph families, is not settled though.

Charge-patterning phase transition on a surface lattice of titratable sites adjacent to an electrolyte solution

NASA Astrophysics Data System (ADS)

Shore, Joel; Thurston, George

We discuss a model for a charge-patterning phase transition on a two-dimensional square lattice of titratable sites, here regarded as protonation sites, placed on a square lattice in a dielectric medium just below the planar interface between this medium and an aqueous salt solution. Within Debye-Huckel theory, the analytical form of the electrostatic repulsion between protonated sites exhibits an approximate inverse cubic power-law decrease beyond short distances. The problem can thus be mapped onto the two-dimensional antiferromagnetic Ising model with this longer-range interaction, which we study with Monte Carlo simulations. As we increase pH, the occupation probability of a site decreases from 1 at low pH to 0 at high pH. For sufficiently-strong interaction strengths, a phase transition occurs as the occupation probability of 1/2 is approached: the charges arrange themselves into a checkerboard pattern. This ordered phase persists over a range of pH until a transition occurs back to a disordered state. This state is the analogue of the Neel state in the antiferromagnetic Ising spin model. More complicated ordered phases are expected for sufficiently strong interactions (with occupation probabilities of 1/4 and 3/4) and if the lattice is triangular rather than square. This work was supported by NIH EY018249 (GMT).

Two-dimensional RCFT's without Kac-Moody symmetry

NASA Astrophysics Data System (ADS)

Hampapura, Harsha R.; Mukhi, Sunil

2016-07-01

Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we find "dual" theories whose characters obey bilinear relations with those of the minimal models to give the Moonshine Module. In some ways this relation is analogous to cosets of meromorphic CFT's. The theory dual in this sense to the Ising model has central charge 47/2 and is related to the Baby Monster Module.

Self-organized critical behavior and marginality in Ising spin glasses

NASA Astrophysics Data System (ADS)

Sharma, Auditya; Yeo, Joonhyun; Moore, M. A.

2018-05-01

We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between the spins which falls off as a power σ of their separation. We have made a detailed study in particular of the energies of the states reached in a quench from infinite temperature and their overlaps, including the spin glass susceptibility. In the regime where , where the model is similar to the Sherrington–Kirkpatrick model, we find that the spin glass susceptibility diverges logarithmically with increasing N, the number of spins in the system, whereas for it remains finite. We attribute the behavior for to self-organized critical behavior, where the system after the quench is close to the transition between states which have trivial overlaps and those with the non-trivial overlaps associated with replica symmetry breaking. We have also found by studying the distribution of local fields that the states reached in the quench have marginal stability but only when .

Simulation of magnetoelastic response of iron nanowire loop

NASA Astrophysics Data System (ADS)

Huang, Junping; Peng, Xianghe; Wang, Zhongchang; Hu, Xianzhi

2018-03-01

We analyzed the magnetoelastic responses of one-dimensional iron nanowire loop systems with quantum statistical mechanics, treating the particles in the systems as identical bosons with an arbitrary integer spin. Under the assumptions adopted, we demonstrated that the Hamiltonian of the system can be separated into two parts, corresponding to two Ising subsystems, describing the particle spin and the particle displacement, respectively. Because the energy of the particle motion at atomic scale is quantized, there should be more the strict constraint on the particle displacement Ising subsystem. Making use of the existing results for Ising system, the partition function of the system was derived into two parts, corresponding respectively to the two Ising subsystems. Then the Gibbs distribution was obtained by statistical mechanics, and the description for the magnetoelastic response was derived. The magnetoelastic responses were predicted with the developed approach, and the comparison with the results calculated with VASP demonstrates the validity of the developed approach.

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.

Networked Ising-Sznajd AR-β Model

NASA Astrophysics Data System (ADS)

Nagao, Tomonori; Ohmiya, Mayumi

2009-09-01

The modified Ising-Sznajd model is studied to clarify the machanism of price formation in the stock market. The conventional Ising-Sznajd model is improved as a small world network with the rewireing probability β(t) which depends on the time. Numerical experiments show that phase transition, regarded as a economical crisis, is inevitable in this model.

Disorder from order among anisotropic next-nearest-neighbor Ising spin chains in SrHo 2O 4

DOE PAGES

Wen, J. -J.; Tian, W.; Garlea, V. O.; ...

2015-02-26

In this study, we describe why Ising spin chains with competing interactions in SrHo 2O 4 segregate into ordered and disordered ensembles at low temperatures (T). Using elastic neutron scattering, magnetization, and specific heat measurements, the two distinct spin chains are inferred to have Néel (↑↓↑↓) and double-Néel (↑↑↓↓) ground states, respectively. Below T N = 0.68(2)K, the Néel chains develop three-dimensional long range order (LRO), which arrests further thermal equilibration of the double-Néel chains so they remain in a disordered incommensurate state for T below T S = 0.52(2)K. SrHo 2O 4 distills an important feature of incommensurate lowmore » dimensional magnetism: kinetically trapped topological defects in a quasi–d–dimensional spin system can preclude order in d + 1 dimensions.« less

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.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Bayesian feature selection for high-dimensional linear regression via the Ising approximation with applications to genomics.

PubMed

Fisher, Charles K; Mehta, Pankaj

2015-06-01

Feature selection, identifying a subset of variables that are relevant for predicting a response, is an important and challenging component of many methods in statistics and machine learning. Feature selection is especially difficult and computationally intensive when the number of variables approaches or exceeds the number of samples, as is often the case for many genomic datasets. Here, we introduce a new approach--the Bayesian Ising Approximation (BIA)-to rapidly calculate posterior probabilities for feature relevance in L2 penalized linear regression. In the regime where the regression problem is strongly regularized by the prior, we show that computing the marginal posterior probabilities for features is equivalent to computing the magnetizations of an Ising model with weak couplings. Using a mean field approximation, we show it is possible to rapidly compute the feature selection path described by the posterior probabilities as a function of the L2 penalty. We present simulations and analytical results illustrating the accuracy of the BIA on some simple regression problems. Finally, we demonstrate the applicability of the BIA to high-dimensional regression by analyzing a gene expression dataset with nearly 30 000 features. These results also highlight the impact of correlations between features on Bayesian feature selection. An implementation of the BIA in C++, along with data for reproducing our gene expression analyses, are freely available at http://physics.bu.edu/∼pankajm/BIACode. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

The initial subevent of the 1994 Northridge, California, earthquake: Is earthquake size predictable?

USGS Publications Warehouse

Kilb, Debi; Gomberg, J.

1999-01-01

We examine the initial subevent (ISE) of the M?? 6.7, 1994 Northridge, California, earthquake in order to discriminate between two end-member rupture initiation models: the 'preslip' and 'cascade' models. Final earthquake size may be predictable from an ISE's seismic signature in the preslip model but not in the cascade model. In the cascade model ISEs are simply small earthquakes that can be described as purely dynamic ruptures. In this model a large earthquake is triggered by smaller earthquakes; there is no size scaling between triggering and triggered events and a variety of stress transfer mechanisms are possible. Alternatively, in the preslip model, a large earthquake nucleates as an aseismically slipping patch in which the patch dimension grows and scales with the earthquake's ultimate size; the byproduct of this loading process is the ISE. In this model, the duration of the ISE signal scales with the ultimate size of the earthquake, suggesting that nucleation and earthquake size are determined by a more predictable, measurable, and organized process. To distinguish between these two end-member models we use short period seismograms recorded by the Southern California Seismic Network. We address questions regarding the similarity in hypocenter locations and focal mechanisms of the ISE and the mainshock. We also compare the ISE's waveform characteristics to those of small earthquakes and to the beginnings of earthquakes with a range of magnitudes. We find that the focal mechanisms of the ISE and mainshock are indistinguishable, and both events may have nucleated on and ruptured the same fault plane. These results satisfy the requirements for both models and thus do not discriminate between them. However, further tests show the ISE's waveform characteristics are similar to those of typical small earthquakes in the vicinity and more importantly, do not scale with the mainshock magnitude. These results are more consistent with the cascade model.

Quantum Criticality of an Ising-like Spin-1 /2 Antiferromagnetic Chain in a Transverse Magnetic Field

NASA Astrophysics Data System (ADS)

Wang, Zhe; Lorenz, T.; Gorbunov, D. I.; Cong, P. T.; Kohama, Y.; Niesen, S.; Breunig, O.; Engelmayer, J.; Herman, A.; Wu, Jianda; Kindo, K.; Wosnitza, J.; Zherlitsyn, S.; Loidl, A.

2018-05-01

We report on magnetization, sound-velocity, and magnetocaloric-effect measurements of the Ising-like spin-1 /2 antiferromagnetic chain system BaCo2V2O8 as a function of temperature down to 1.3 K and an applied transverse magnetic field up to 60 T. While across the Néel temperature of TN˜5 K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature the field-dependent measurements reveal a sharp softening of sound velocity v (B ) and a clear minimum of temperature T (B ) at B⊥c,3 D=21.4 T , indicating the suppression of the antiferromagnetic order. At higher fields, the T (B ) curve shows a broad minimum at B⊥c=40 T , accompanied by a broad minimum in the sound velocity and a saturationlike magnetization. These features signal a quantum phase transition, which is further characterized by the divergent behavior of the Grüneisen parameter ΓB∝(B -B⊥c)-1. By contrast, around the critical field, the Grüneisen parameter converges as temperature decreases, pointing to a quantum critical point of the one-dimensional transverse-field Ising model.

Local characterization of one-dimensional topologically ordered states

NASA Astrophysics Data System (ADS)

Cui, Jian; Amico, Luigi; Fan, Heng; Gu, Mile; Hamma, Alioscia; Vedral, Vlatko

2013-09-01

We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. We show that ground states within the topological phase cannot be connected with each other through local operations and classical communication between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Rényi entropies of different physical systems that provide examples for symmetry-protected topological phases. Specifically, we consider the spin-1/2 cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for symmetry-protected topological order. Since the picture holds even at the system's local scale, our analysis can serve as a local experimental test for topological order.

Anomalous metastability in a temperature-driven transition

NASA Astrophysics Data System (ADS)

Ibáñez Berganza, M.; Coletti, P.; Petri, A.

2014-06-01

The Langer theory of metastability provides a description of the lifetime and properties of the metastable phase of the Ising model field-driven transition, describing the magnetic-field-driven transition in ferromagnets and the chemical-potential-driven transition of fluids. An immediate further step is to apply it to the study of a transition driven by the temperature, as the one exhibited by the two-dimensional Potts model. For this model, a study based on the analytical continuation of the free energy (Meunier J. L. and Morel A., Eur. Phys. J. B, 13 (2000) 341) predicts the anomalous vanishing of the metastable temperature range in the large-system-size limit, an issue that has been controversial since the eighties. By a GPU algorithm we compare the Monte Carlo dynamics with the theory. For temperatures close to the transition we obtain agreement and characterize the dependence on the system size, which is essentially different with respect to the Ising case. For smaller temperatures, we observe the onset of stationary states with non-Boltzmann statistics, not predicted by the theory.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

Out-of-time-ordered correlators in a quantum Ising chain

NASA Astrophysics Data System (ADS)

Lin, Cheng-Ju; Motrunich, Olexei I.

2018-04-01

Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a "shell-like" structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t-1 power law at long time t . On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like" structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t-1 /4 for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a "ball-like" structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Crystal structure and partial Ising-like magnetic ordering of orthorhombic D y 2 Ti O 5

DOE PAGES

Shamblin, Jacob; Calder, Stuart; Dun, Zhiling; ...

2016-07-12

The structure and magnetic properties of orthorhombic Dy 2TiO 5 have been investigated using x-ray diffraction, neutron diffraction, and alternating current (ac)/direct current (dc) magnetic susceptibility measurements. In this paper, we report a continuous structural distortion below 100 K characterized by negative thermal expansion in the [0 1 0] direction. Neutron diffraction and magnetic susceptibility measurements revealed that two-dimensional (2D) magnetic ordering begins at 3.1 K, which is followed by a three-dimensional magnetic transition at 1.7 K. The magnetic structure has been solved through a representational analysis approach and can be indexed with the propagation vector k = [0 1/2more » 0]. The spin structure corresponds to a coplanar model of interwoven 2D “sheets” extending in the [0 1 0] direction. The local crystal field is different for each Dy 3+ ion (Dy1 and Dy2), one of which possesses strong uniaxial symmetry indicative of Ising-like magnetic ordering. In conclusion, consequently, two succeeding transitions under magnetic field are observed in the ac susceptibility, which are associated with flipping each Dy 3+ spin independently.« less

ISEE 1 charged particle observations indicative of open magnetospheric field lines near the subsolar region

NASA Technical Reports Server (NTRS)

Williams, D. J.; Frank, L. A.

1980-01-01

On November 20, 1977, at 0230-0300 UT, ISEE 1 encountered unusual charged particle distributions within the magnetosphere. The three-dimensional distribution observations for energetic (greater than 24 keV) ions and plasma show the development of field-aligned asymmetries in the energetic ion distributions simultaneously with a marked change in plasma flow. It is concluded that the most likely explanation for these observations is that ISEE 1 encountered open magnetospheric field lines at its position within the magnetosphere (1030 LT and 1200 plus or minus 300 km from the magnetopause). Field lines were open near the geomagnetic equator, and the geometry was spatially or temporally variable. Other features of the field line topology are presented.

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.

Towards Simulating the Transverse Ising Model in a 2D Array of Trapped Ions

NASA Astrophysics Data System (ADS)

Sawyer, Brian

2013-05-01

Two-dimensional Coulomb crystals provide a useful platform for large-scale quantum simulation. Penning traps enable confinement of large numbers of ions (>100) and allow for the tunable-range spin-spin interactions demonstrated in linear ion strings, facilitating simulation of quantum magnetism at a scale that is currently intractable on classical computers. We readily confine hundreds of Doppler laser-cooled 9Be+ within a Penning trap, producing a planar array of ions with self-assembled triangular order. The transverse ``drumhead'' modes of our 2D crystal along with the valence electron spin of Be+ serve as a resource for generating spin-motion and spin-spin entanglement. Applying a spin-dependent optical dipole force (ODF) to the ion array, we perform spectroscopy and thermometry of individual drumhead modes. This ODF also allows us to engineer long-range Ising spin couplings of either ferromagnetic or anti-ferromagnetic character whose approximate power-law scaling with inter-ion distance, d, may be varied continuously from 1 /d0 to 1 /d3. An effective transverse magnetic field is applied via microwave radiation at the ~124-GHz spin-flip frequency, and ground states of the effective Ising Hamiltonian may in principle be prepared adiabatically by slowly decreasing this transverse field in the presence of the induced Ising coupling. Long-range anti-ferromagnetic interactions are of particular interest due to their inherent spin frustration and resulting large, near-degenerate manifold of ground states. We acknowledge support from NIST and the DARPA-OLE program.

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.

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

NASA Astrophysics Data System (ADS)

Flores-Sola, Emilio J.; Berche, Bertrand; Kenna, Ralph; Weigel, Martin

2015-01-01

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour by simulating one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Compressed quantum computation using a remote five-qubit quantum computer

NASA Astrophysics Data System (ADS)

Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.

2017-05-01

The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.

Thermal conductivity of Ca3Co2O6 single crystals

NASA Astrophysics Data System (ADS)

Che, H. L.; Shi, J.; Wu, J. C.; Rao, X.; Liu, X. G.; Zhao, X.; Sun, X. F.

2018-05-01

Ca3Co2O6 is a rare example of one-dimensional Ising spin-chain material with the moments preferentially aligned along the c axis. In this work, we study the c-axis thermal conductivity (κc) of Ca3Co2O6 single crystal at low temperatures down to 0.3 K and in magnetic fields up to 14 T. The zero-field κc(T) shows a large phonon peak and can be well fitted by using the classical Debye model, which indicates that the heat transport is purely phononic. Moreover, the low-T κc(H) isotherms with H || c display a field-independent behavior. These results indicate that there is no contribution of magnetic excitations to the thermal conductivity in Ca3Co2O6, neither carrying heat nor scattering phonons, which can be attributed to the Ising-like spin anisotropy.

Probing strong correlations with light scattering: Example of the quantum Ising model

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2016-10-01

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Probing strong correlations with light scattering: Example of the quantum Ising model

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

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Tax Evasion and Nonequilibrium Model on Apollonian Networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2012-11-01

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

NASA Astrophysics Data System (ADS)

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; O'Brien, Liam; Watts, Justin D.; Manno, Michael; Leighton, Chris; Scholl, Andreas; Nisoli, Cristiano; Schiffer, Peter

2016-02-01

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments. The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

DOE PAGES

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; ...

2015-10-26

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments.more » The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.« less

From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

Corruption dynamics model

NASA Astrophysics Data System (ADS)

Malafeyev, O. A.; Nemnyugin, S. A.; Rylow, D.; Kolpak, E. P.; Awasthi, Achal

2017-07-01

The corruption dynamics is analyzed by means of the lattice model which is similar to the three-dimensional Ising model. Agents placed at nodes of the corrupt network periodically choose to perfom or not to perform the act of corruption at gain or loss while making decisions based on the process history. The gain value and its dynamics are defined by means of the Markov stochastic process modelling with parameters established in accordance with the influence of external and individual factors on the agent's gain. The model is formulated algorithmically and is studied by means of the computer simulation. Numerical results are obtained which demonstrate asymptotic behaviour of the corruption network under various conditions.

Toward an Ising Model of Cancer and Beyond

PubMed Central

Torquato, Salvatore

2011-01-01

The holy grail of tumor modeling is to formulate theoretical and computational tools that can be utilized in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth. In order to develop such a predictive model, one must account for the numerous complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an “Ising model” of cancer. The Ising model is an idealized statistical-mechanical model of ferromagnetism that is based on simple local-interaction rules, but nonetheless leads to basic insights and features of real magnets, such as phase transitions with a critical point. The review begins with a description of a minimalist four-dimensional (three dimensions in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment, including induced resistance, is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. A discussion about the need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented. Finally, we propose the possibility of using optimization techniques, which have been used profitably to understand physical phenomena, in order to devise therapeutic (chemotherapy/radiation) strategies and to understand tumorigenesis itself. PMID:21301063

Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics

NASA Astrophysics Data System (ADS)

Godrèche, Claude; Pleimling, Michel

2018-04-01

We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics correspond to two limits of the directed Ising model, defined by rules that break the full symmetry of the former, yet sharing the same Boltzmann-Gibbs distribution at stationarity. In one of these limits the directed Ising model is reversible, in the other one it is irreversible. For the kinetic Ising-Glauber model, several recent studies have demonstrated the role of critical percolation to predict the probabilities for the system to reach the ground state or to fall in a metastable state. We investigate to what extent the predictions coming from critical percolation still apply to the two other dynamics.

Simple universal models capture all classical spin physics.

PubMed

De las Cuevas, Gemma; Cubitt, Toby S

2016-03-11

Spin models are used in many studies of complex systems because they exhibit rich macroscopic behavior despite their microscopic simplicity. Here, we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain "universal models," with at most polynomial overhead. This holds for classical models with discrete or continuous degrees of freedom. We prove necessary and sufficient conditions for a spin model to be universal and show that one of the simplest and most widely studied spin models, the two-dimensional Ising model with fields, is universal. Our results may facilitate physical simulations of Hamiltonians with complex interactions. Copyright © 2016, American Association for the Advancement of Science.

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

NASA Astrophysics Data System (ADS)

Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain; de Léséleuc, Sylvain; Macrì, Tommaso; Lahaye, Thierry; Browaeys, Antoine

2016-06-01

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

Nonequilibrium critical behavior of model statistical systems and methods for the description of its features

NASA Astrophysics Data System (ADS)

Prudnikov, V. V.; Prudnikov, P. V.; Mamonova, M. V.

2017-11-01

This paper reviews features in critical behavior of far-from-equilibrium macroscopic systems and presents current methods of describing them by referring to some model statistical systems such as the three-dimensional Ising model and the two-dimensional XY model. The paper examines the critical relaxation of homogeneous and structurally disordered systems subjected to abnormally strong fluctuation effects involved in ordering processes in solids at second-order phase transitions. Interest in such systems is due to the aging properties and fluctuation-dissipation theorem violations predicted for and observed in systems slowly evolving from a nonequilibrium initial state. It is shown that these features of nonequilibrium behavior show up in the magnetic properties of magnetic superstructures consisting of alternating nanoscale-thick magnetic and nonmagnetic layers and can be observed not only near the film’s critical ferromagnetic ordering temperature Tc, but also over the wide temperature range T ⩽ Tc.

Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

NASA Astrophysics Data System (ADS)

Muttalib, K. A.; Khatun, M.; Barry, J. H.

2017-11-01

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility χ⊥ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled χ⊥ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

Analysis of the phase transition in the two-dimensional Ising ferromagnet using a Lempel-Ziv string-parsing scheme and black-box data-compression utilities

NASA Astrophysics Data System (ADS)

Melchert, O.; Hartmann, A. K.

2015-02-01

In this work we consider information-theoretic observables to analyze short symbolic sequences, comprising time series that represent the orientation of a single spin in a two-dimensional (2D) Ising ferromagnet on a square lattice of size L2=1282 for different system temperatures T . The latter were chosen from an interval enclosing the critical point Tc of the model. At small temperatures the sequences are thus very regular; at high temperatures they are maximally random. In the vicinity of the critical point, nontrivial, long-range correlations appear. Here we implement estimators for the entropy rate, excess entropy (i.e., "complexity"), and multi-information. First, we implement a Lempel-Ziv string-parsing scheme, providing seemingly elaborate entropy rate and multi-information estimates and an approximate estimator for the excess entropy. Furthermore, we apply easy-to-use black-box data-compression utilities, providing approximate estimators only. For comparison and to yield results for benchmarking purposes, we implement the information-theoretic observables also based on the well-established M -block Shannon entropy, which is more tedious to apply compared to the first two "algorithmic" entropy estimation procedures. To test how well one can exploit the potential of such data-compression techniques, we aim at detecting the critical point of the 2D Ising ferromagnet. Among the above observables, the multi-information, which is known to exhibit an isolated peak at the critical point, is very easy to replicate by means of both efficient algorithmic entropy estimation procedures. Finally, we assess how good the various algorithmic entropy estimates compare to the more conventional block entropy estimates and illustrate a simple modification that yields enhanced results.

Quantum simulation of transverse Ising models with Rydberg atoms

NASA Astrophysics Data System (ADS)

Schauss, Peter

2018-04-01

Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

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.

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.

Orthogonal Polynomials on the Unit Circle with Fibonacci Verblunsky Coefficients, II. Applications

NASA Astrophysics Data System (ADS)

Damanik, David; Munger, Paul; Yessen, William N.

2013-10-01

We consider CMV matrices with Verblunsky coefficients determined in an appropriate way by the Fibonacci sequence and present two applications of the spectral theory of such matrices to problems in mathematical physics. In our first application we estimate the spreading rates of quantum walks on the line with time-independent coins following the Fibonacci sequence. The estimates we obtain are explicit in terms of the parameters of the system. In our second application, we establish a connection between the classical nearest neighbor Ising model on the one-dimensional lattice in the complex magnetic field regime, and CMV operators. In particular, given a sequence of nearest-neighbor interaction couplings, we construct a sequence of Verblunsky coefficients, such that the support of the Lee-Yang zeros of the partition function for the Ising model in the thermodynamic limit coincides with the essential spectrum of the CMV matrix with the constructed Verblunsky coefficients. Under certain technical conditions, we also show that the zeros distribution measure coincides with the density of states measure for the CMV matrix.

Nonequilibrium dynamic critical scaling of the quantum Ising chain.

PubMed

Kolodrubetz, Michael; Clark, Bryan K; Huse, David A

2012-07-06

We solve for the time-dependent finite-size scaling functions of the one-dimensional transverse-field Ising chain during a linear-in-time ramp of the field through the quantum critical point. We then simulate Mott-insulating bosons in a tilted potential, an experimentally studied system in the same equilibrium universality class, and demonstrate that universality holds for the dynamics as well. We find qualitatively athermal features of the scaling functions, such as negative spin correlations, and we show that they should be robustly observable within present cold atom experiments.

Long-time predictability in disordered spin systems following a deep quench

NASA Astrophysics Data System (ADS)

Ye, J.; Gheissari, R.; Machta, J.; Newman, C. M.; Stein, D. L.

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit—in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

Long-time predictability in disordered spin systems following a deep quench.

PubMed

Ye, J; Gheissari, R; Machta, J; Newman, C M; Stein, D L

2017-04-01

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

On the number of infinite geodesics and ground states in disordered systems

NASA Astrophysics Data System (ADS)

Wehr, Jan

1997-04-01

We study first-passage percolation models and their higher dimensional analogs—models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to +∞. As corollaries we show that in any dimension d≥2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or +∞. Proofs employ simple large-deviation estimates and ergodic arguments.

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

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Quantum cluster variational method and message passing algorithms revisited

NASA Astrophysics Data System (ADS)

Domínguez, E.; Mulet, Roberto

2018-02-01

We present a general framework to study quantum disordered systems in the context of the Kikuchi's cluster variational method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard application of the Kikuchi's CVM can be easily translated to message passing equations for specific instances of the disordered system. We then present an "ad hoc" extension of these equations to a population dynamic algorithm representing an average case scenario. At the Bethe level, these equations are equivalent to the dynamic population equations that can be derived from a proper cavity ansatz. However, at the plaquette approximation, the interpretation is more subtle and we discuss it taking also into account previous results in classical disordered models. Moreover, we develop a formalism to properly deal with the average case scenario using a replica-symmetric ansatz within this CVM for quantum disordered systems. Finally, we present and discuss numerical solutions of the different approximations for the quantum transverse Ising model and the quantum random field Ising model in two-dimensional lattices.

Thermodynamics of Ising spins on the triangular kagome lattice: Exact analytical method and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Loh, Y. L.; Yao, D. X.; Carlson, E. W.

2008-04-01

A new class of two-dimensional magnetic materials Cu9X2(cpa)6ṡxH2O ( cpa=2 -carboxypentonic acid; X=F,Cl,Br ) was recently fabricated in which Cu sites form a triangular kagome lattice (TKL). As the simplest model of geometric frustration in such a system, we study the thermodynamics of Ising spins on the TKL using exact analytic method as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice magnetizations, and susceptibility. We describe the rich phase diagram of the model as a function of coupling constants, temperature, and applied magnetic field. For frustrated interactions in the absence of applied field, the ground state is a spin liquid phase with residual entropy per spin s0/kB=(1)/(9)ln72≈0.4752… . In weak applied field, the system maps to the dimer model on a honeycomb lattice, with residual entropy 0.0359 per spin and quasi-long-range order with power-law spin-spin correlations that should be detectable by neutron scattering. The power-law correlations become exponential at finite temperatures, but the correlation length may still be long.

Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions

NASA Astrophysics Data System (ADS)

de Souza, S. M.; Rojas, Onofre

2018-01-01

There are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of chain structures, which exhibit unexpected behaviors quite similar to the first and second order phase transition, which could be confused naively with an authentic phase transition. Through the analysis of the first derivative of free energy, such as entropy, magnetization, and internal energy, a "sudden" jump that closely resembles a first-order phase transition at finite temperature occurs. However, by analyzing the second derivative of free energy, such as specific heat and magnetic susceptibility at finite temperature, it behaves quite similarly to a second-order phase transition exhibiting an astonishingly sharp and fine peak. The correlation length also confirms the evidence of this pseudo-transition temperature, where a sharp peak occurs at the pseudo-critical temperature. We also present the necessary conditions for the emergence of these quasi-phases and pseudo-transitions.

Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets

NASA Astrophysics Data System (ADS)

Bibikov, P. N.

2018-04-01

Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice. Dedicated to the memory of L D Faddeev.

The Ising model coupled to 2d orders

NASA Astrophysics Data System (ADS)

Glaser, Lisa

2018-04-01

In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase diagram in terms of the Wick rotation parameter β and the Ising coupling j and find that the matter and the causal sets together give rise to an interesting phase structure. The couplings give rise to five different phases. The causal sets take on random or crystalline characteristics as described in Surya (2012 Class. Quantum Grav. 29 132001) and the Ising model can be correlated or uncorrelated on the random orders and correlated, uncorrelated or anti-correlated on the crystalline orders. We find that at least one new phase transition arises, in which the Ising spins push the causal set into the crystalline phase.

Ising Criticality of the Clock Model from Density of States Obtained by the Replica Exchange-Wang-Landau Method

NASA Astrophysics Data System (ADS)

Cadilhe, Antonio

2018-04-01

We performed extensive simulations, using the Replica Exchange-Wang-Landau method, of the clock model for orders 3 and 4 on a square lattice, where critical behaviors are expected to belong to the Ising universality class. Though order 2 represents the Ising model, thus, being exactly solvable in two-dimensions, we still provide such results for comparison to the other two orders. Results for various energy related quantities such as the mean energy per spin, specific heat, as well as logarithm scaling of the peak of the specific heat are presented and shown to follow Ising behavior. Additionally, we also present results related to magnetic quantities, such as the magnetization, magnetic susceptibility, and corresponding scaling behavior of the peak of the magnetic susceptibility. Again, our results show scaling in conformity to Ising critical behavior.

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

NASA Astrophysics Data System (ADS)

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

2017-06-01

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models—the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional X Y model—and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (X Y model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Effective potential of the three-dimensional Ising model: The pseudo-ɛ expansion study

NASA Astrophysics Data System (ADS)

Sokolov, A. I.; Kudlis, A.; Nikitina, M. A.

2017-08-01

The ratios R2k of renormalized coupling constants g2k that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar λϕ4 field theory (3D Ising model) within the pseudo-ɛ expansion approach. Pseudo-ɛ expansions for the critical values of g6, g8, g10, R6 =g6 / g42, R8 =g8 / g43 and R10 =g10 / g44 originating from the five-loop renormalization group (RG) series are derived. Pseudo-ɛ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé-Borel-Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values R6* = 1.6488 and R6* = 1.6490 which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-ɛ expansions is less favorable. Nevertheless, the conform-Borel resummation gives R8* = 0.868, the number being close to the lattice estimate R8* = 0.871 and compatible with the result of 3D RG analysis R8* = 0.857. Pseudo-ɛ expansions for R10* and g10* are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

Nonequilibrium umbrella sampling in spaces of many order parameters

NASA Astrophysics Data System (ADS)

Dickson, Alex; Warmflash, Aryeh; Dinner, Aaron R.

2009-02-01

We recently introduced an umbrella sampling method for obtaining nonequilibrium steady-state probability distributions projected onto an arbitrary number of coordinates that characterize a system (order parameters) [A. Warmflash, P. Bhimalapuram, and A. R. Dinner, J. Chem. Phys. 127, 154112 (2007)]. Here, we show how our algorithm can be combined with the image update procedure from the finite-temperature string method for reversible processes [E. Vanden-Eijnden and M. Venturoli, "Revisiting the finite temperature string method for calculation of reaction tubes and free energies," J. Chem. Phys. (in press)] to enable restricted sampling of a nonequilibrium steady state in the vicinity of a path in a many-dimensional space of order parameters. For the study of transitions between stable states, the adapted algorithm results in improved scaling with the number of order parameters and the ability to progressively refine the regions of enforced sampling. We demonstrate the algorithm by applying it to a two-dimensional model of driven Brownian motion and a coarse-grained (Ising) model for nucleation under shear. It is found that the choice of order parameters can significantly affect the convergence of the simulation; local magnetization variables other than those used previously for sampling transition paths in Ising systems are needed to ensure that the reactive flux is primarily contained within a tube in the space of order parameters. The relation of this method to other algorithms that sample the statistics of path ensembles is discussed.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

NASA Astrophysics Data System (ADS)

Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando; Preskill, John; Svore, Krysta M.

2018-05-01

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p3DCC (1 )≃1.9 % and p3DCC (2 )≃27.6 % . We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Magnetopause modeling - Flux transfer events and magnetosheath quasi-trapped distributions

NASA Technical Reports Server (NTRS)

Speiser, T. W.; Williams, D. J.

1982-01-01

Three-dimensional distribution functions for energetic ions are studied numerically in the magnetosphere, through the magnetopause, and in the magnetosheath using a simple one-dimensional quasi-static model and ISEE 1 magnetopause crossing data for November 10, 1977. Quasi-trapped populations in the magnetosheath observed near flux transfer events (FTEs) are investigated, and it is shown that the population in the sheath appears to sandwich the FTE distributions. These quasi-trapped distributions are due to slow, large pitch angle, outward moving particles left behind by the outward rush of the ions more field-aligned at the time the flux was opened. It is found that sheath convective flows can map along the connected flux tube without drastically changing the distribution function, and results suggest that localized tangential fields above the upper limit may exist.

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.

On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions

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

Coffey, Mark W.

2008-04-15

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C{sup Tet}{identical_to}C(1,1) has been of interest from many points of view, with several representations and conjectures having been given in the literature. We prove a conjectured exponentially fast convergent sum for C(1,1), as well as a previously empirical relation for C(1,1) as a remarkable difference of Clausen function values. Our presentation includes propositions extending the theory of the dilogarithm Li{sub 2} and Clausen Cl{sub 2} functions,more » as well as their relation to other special functions of mathematical physics. The results strengthen connections between Feynman diagram integrals, volumes in hyperbolic space, number theory, and special functions and numbers, specifically including dilogarithms, Clausen function values, and harmonic numbers.« less

Floating phase in the one-dimensional transverse axial next-nearest-neighbor Ising model.

PubMed

Chandra, Anjan Kumar; Dasgupta, Subinay

2007-02-01

To study the ground state of an axial next-nearest-neighbor Ising chain under transverse field as a function of frustration parameter kappa and field strength Gamma, we present here two different perturbative analyses. In one, we consider the (known) ground state at kappa=0.5 and Gamma=0 as the unperturbed state and treat an increase of the field from 0 to Gamma coupled with an increase of kappa from 0.5 to 0.5+rGamma/J as perturbation. The first-order perturbation correction to eigenvalue can be calculated exactly and we could conclude that there are only two phase-transition lines emanating from the point kappa=0.5, Gamma=0. In the second perturbation scheme, we consider the number of domains of length 1 as the perturbation and obtain the zeroth-order eigenfunction for the perturbed ground state. From the longitudinal spin-spin correlation, we conclude that floating phase exists for small values of transverse field over the entire region intermediate between the ferromagnetic phase and antiphase.

Reentrant behavior in the nearest-neighbor Ising antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Neto, Minos A.; de Sousa, J. Ricardo

2004-12-01

Motived by the H-T phase diagram in the bcc Ising antiferromagnetic with nearest-neighbor interactions obtained by Monte Carlo simulation [Landau, Phys. Rev. B 16, 4164 (1977)] that shows a reentrant behavior at low temperature, with two critical temperatures in magnetic field about 2% greater than the critical value Hc=8J , we apply the effective field renormalization group (EFRG) approach in this model on three-dimensional lattices (simple cubic-sc and body centered cubic-bcc). We find that the critical curve TN(H) exhibits a maximum point around of H≃Hc only in the bcc lattice case. We also discuss the critical behavior by the effective field theory in clusters with one (EFT-1) and two (EFT-2) spins, and a reentrant behavior is observed for the sc and bcc lattices. We have compared our results of EFRG in the bcc lattice with Monte Carlo and series expansion, and we observe a good accordance between the methods.

Fluctuation in the Intermediate Magnetic Phase of Triangular Ising Antiferromagnet (CeS)1.16[Fe0.33(NbS2)2

NASA Astrophysics Data System (ADS)

Michioka, Chishiro; Suzuki, Kazuya; Mibu, Ko

2002-10-01

We applied 57Fe Mössbauer spectroscopy for investigating the Ising spin triangular lattice antiferromagnet (TLA) (CeS)1.16[Fe0.33(NbS2)2] between 2 and 300 K. The spectra revealed that the relaxation time of the hyperfine field markedly changes in the intermediate phase between TN1=22 K and TN2=15 K due to strong spin fluctuation. The relaxation of the hyperfine field is not sufficiently fast as a paramagnet even at 77 K, which is much higher than TN1, and the inverse susceptibility of (LaS)1.14[Fe0.33(NbS2)2] deviates from the Curie-Weiss law below 100 K. These results indicate that an unusual short-range order exists above TN1. The temperature dependence of the Mössbauer spectra can be explained by phase transition of the three-dimensional TLA model with weak interlayer exchange interactions.

Statistical mechanics of the cluster Ising model

NASA Astrophysics Data System (ADS)

Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko

2011-08-01

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.

Volatility behavior of visibility graph EMD financial time series from Ising interacting system

NASA Astrophysics Data System (ADS)

Zhang, Bo; Wang, Jun; Fang, Wen

2015-08-01

A financial market dynamics model is developed and investigated by stochastic Ising system, where the Ising model is the most popular ferromagnetic model in statistical physics systems. Applying two graph based analysis and multiscale entropy method, we investigate and compare the statistical volatility behavior of return time series and the corresponding IMF series derived from the empirical mode decomposition (EMD) method. And the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, we find that the degree distribution of visibility graph for the simulation series has the power law tails, and the assortative network exhibits the mixing pattern property. All these features are in agreement with the real market data, the research confirms that the financial model established by the Ising system is reasonable.

Interplay of interfacial noise and curvature-driven dynamics in two dimensions

NASA Astrophysics Data System (ADS)

Roy, Parna; Sen, Parongama

2017-02-01

We explore the effect of interplay of interfacial noise and curvature-driven dynamics in a binary spin system. An appropriate model is the generalized two-dimensional voter model proposed earlier [M. J. de Oliveira, J. F. F. Mendes, and M. A. Santos, J. Phys. A: Math. Gen. 26, 2317 (1993), 10.1088/0305-4470/26/10/006], where the flipping probability of a spin depends on the state of its neighbors and is given in terms of two parameters, x and y . x =0.5 andy =1 correspond to the conventional voter model which is purely interfacial noise driven, while x =1 and y =1 correspond to the Ising model, where coarsening is fully curvature driven. The coarsening phenomena for 0.5 0.5 ; the effect of x appears in altering the value of the parameter occurring in the scaling function only.

Spin flip statistics and spin wave interference patterns in Ising ferromagnetic films: A Monte Carlo study.

PubMed

Acharyya, Muktish

2017-07-01

The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.

Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co 3V 2O 8 in a transverse magnetic field

DOE PAGES

Fritsch, Katharina; Ehlers, G.; Rule, K. C.; ...

2015-11-05

We study the application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional kagome staircase magnet, Co 3V 2O 8, induces three quantum phase transitions at low temperatures, ultimately producing a novel high field polarized state, with two distinct sublattices. New time-of-flight neutron scattering techniques, accompanied by large angular access, high magnetic field infrastructure allow the mapping of a sequence of ferromagnetic and incommensurate phases and their accompanying spin excitations. Also, at least one of the transitions to incommensurate phases at μ 0H c1~6.25 T and μ 0H c2~7 T is discontinuous, while the finalmore » quantum critical point at μ 0H c3~13 T is continuous.« less

Engineered spin-spin interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joe; Sawyer, Brian; Bollinger, John

2013-05-01

We work with laser cooled 9Be+ ions confined in a Penning trap to simulate quantum magnetic interactions. The valence electron of each ion behaves as an ideal spin- 1 / 2 particle. We recently demonstrated a uniform anti-ferromagnetic Ising interaction on a naturally occurring two-dimensional (2D) triangular crystal of 100 < N < 350 ions. The Ising interaction is generated by a spin-dependent optical dipole force (ODF). For spins separated by distance d, we show that the range can be tuned according to (d / d 0)-a, for 0 < a < 3 . For different operating parameters we can also generate an infinite range ferromagnetic Ising interaction. We also use the ODF for spectroscopy and thermometry of the normal modes of the trapped ion array. A detailed understanding of the modes is important because they mediate the spin-spin interactions. This work is supported by NIST and the DARPA OLE program.

Work Plan for Three-Dimensional Time-Varying, Hydrodynamic and Water Quality Model of Chesapeake Bay

DTIC Science & Technology

1988-08-01

successfully calibrated: a. Dissolved oxygen b. Anmonium c. Nitrate d . Dissolved inorganic phosphorus e. Silica f. Methane g. Sulfide Fluxes of dissolved...oxygen, amonium , nitrate , methane, and sulfide can be related to the rate of diagenesis. A less mechanistic, more empirical approach may be required...CLASSc;CA’ ON A ’I.ORITV 3 D.S1R RUT ON AVA LABMLTY OF REPORT ’b D LASPCTO1,DONGRANG C ED, kApproved for public rele~ise; distribution 2b DC~ASFAT.N

Ising game: Nonequilibrium steady states of resource-allocation systems

NASA Astrophysics Data System (ADS)

Xin, C.; Yang, G.; Huang, J. P.

2017-04-01

Resource-allocation systems are ubiquitous in the human society. But how external fields affect the state of such systems remains poorly explored due to the lack of a suitable model. Because the behavior of spins pursuing energy minimization required by physical laws is similar to that of humans chasing payoff maximization studied in game theory, here we combine the Ising model with the market-directed resource-allocation game, yielding an Ising game. Based on the Ising game, we show theoretical, simulative and experimental evidences for a formula, which offers a clear expression of nonequilibrium steady states (NESSs). Interestingly, the formula also reveals a convertible relationship between the external field (exogenous factor) and resource ratio (endogenous factor), and a class of saturation as the external field exceeds certain limits. This work suggests that the Ising game could be a suitable model for studying external-field effects on resource-allocation systems, and it could provide guidance both for seeking more relations between NESSs and equilibrium states and for regulating human systems by choosing NESSs appropriately.

Learning planar Ising models

DOE PAGES

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; ...

2016-12-01

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Learning planar Ising models

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

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

DOE PAGES

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

2016-11-23

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Critical excitation spectrum of a quantum chain with a local three-spin coupling.

PubMed

McCabe, John F; Wydro, Tomasz

2011-09-01

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.

Physics and financial economics (1776-2014): puzzles, Ising and agent-based models.

PubMed

Sornette, Didier

2014-06-01

This short review presents a selected history of the mutual fertilization between physics and economics--from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the 'Emerging Intelligence Market Hypothesis' to reconcile the pervasive presence of 'noise traders' with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.

Physics and financial economics (1776-2014): puzzles, Ising and agent-based models

NASA Astrophysics Data System (ADS)

Sornette, Didier

2014-06-01

This short review presents a selected history of the mutual fertilization between physics and economics—from Isaac Newton and Adam Smith to the present. The fundamentally different perspectives embraced in theories developed in financial economics compared with physics are dissected with the examples of the volatility smile and of the excess volatility puzzle. The role of the Ising model of phase transitions to model social and financial systems is reviewed, with the concepts of random utilities and the logit model as the analog of the Boltzmann factor in statistical physics. Recent extensions in terms of quantum decision theory are also covered. A wealth of models are discussed briefly that build on the Ising model and generalize it to account for the many stylized facts of financial markets. A summary of the relevance of the Ising model and its extensions is provided to account for financial bubbles and crashes. The review would be incomplete if it did not cover the dynamical field of agent-based models (ABMs), also known as computational economic models, of which the Ising-type models are just special ABM implementations. We formulate the ‘Emerging Intelligence Market Hypothesis’ to reconcile the pervasive presence of ‘noise traders’ with the near efficiency of financial markets. Finally, we note that evolutionary biology, more than physics, is now playing a growing role to inspire models of financial markets.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping.

PubMed

Kubica, Aleksander; Beverland, Michael E; Brandão, Fernando; Preskill, John; Svore, Krysta M

2018-05-04

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_{3DCC}^{(1)}≃1.9% and p_{3DCC}^{(2)}≃27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

de Almeida-Thouless instability in short-range Ising spin glasses

NASA Astrophysics Data System (ADS)

Singh, R. R. P.; Young, A. P.

2017-07-01

We use high-temperature series expansions to study the ±J Ising spin glass in a magnetic field in d -dimensional hypercubic lattices for d =5 -8 and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable w =tanh2J /T for arbitrary values of u =tanh2h /T complete to order w10. We find that the scaling dimension Δ associated with the ordering-field h2 equals 2 in the SK model and for d ≥6 . However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985), 10.1103/PhysRevLett.54.1063], there is a violation of scaling in a finite field, leading to an anomalous h -T dependence of the de Almeida-Thouless (AT) [J. Phys. A 11, 983 (1978), 10.1088/0305-4470/11/5/028] line in high dimensions, whereas scaling is restored as d →6 . Within the convergence of our series analysis, we present evidence supporting an AT line in d ≥6 . In d =5 , the exponents γ and Δ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in d =5 .

Engineered long-range interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joseph W.; Sawyer, Brian C.; Bollinger, John J.; Freericks, James K.

2014-03-01

Ising interactions are one paradigm used to model quantum magnetism in condensed matter systems. At NIST Boulder we confine and Doppler laser cool hundreds of 9Be+ ions in a Penning trap. The valence electron of each ion behaves as an ideal spin-1/2 particle and, in the limit of weak radial confinement relative to axial confinement, the ions naturally form a two-dimensional triangular lattice. A variable-range anti-ferromagnetic Ising interaction is engineered with a spin-dependent optical dipole force (ODF) through spin-dependent excitation of collective modes of ion motion. We have also exploited this spin-dependent force to perform spectroscopy and thermometry of the normal modes of the trapped ion crystal. The high spin-count and long-range spin-spin couplings achievable in the NIST Penning trap brings within reach simulation of computationally intractable problems in quantum magnetism. Examples include modeling quantum magnetic phase transitions and propagation of spin correlations resulting from a quantum quench. The Penning system may also be amenable to observation of spin-liquid behavior thought to arise in systems where the underlying lattice structure can frustrate long-range ordering. Supported by DARPA OLE and NIST.

Emergent equilibrium in many-body optical bistability

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Niroula, Pradeep; Young, Jeremy; Hafezi, Mohammad; Gorshkov, Alexey; Wilson, Ryan; Maghrebi, Mohammad

2017-04-01

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to Rydberg gases, establishing a fascinating interface between traditional many-body physics and the non-equilibrium setting of cavity-QED. At this interface the standard intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. We study the driven-dissipative Bose-Hubbard model, a minimal description of atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability-a foundational and patently non-equilibrium model of cavity-QED-the steady state possesses an emergent equilibrium description in terms of an Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model. M.F.M., J.T.Y., and A.V.G. acknowledge support by ARL CDQI, ARO MURI, NSF QIS, ARO, NSF PFC at JQI, and AFOSR. R.M.W. acknowledges partial support from the NSF under Grant No. PHYS-1516421. M.H. acknowledges support by AFOSR-MURI, ONR and Sloan Foundation.

Bipartite charge fluctuations in one-dimensional Z2 superconductors and insulators

NASA Astrophysics Data System (ADS)

Herviou, Loïc; Mora, Christophe; Le Hur, Karyn

2017-09-01

Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional Z2 (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the X Y Z model.

Phase transitions in Ising models on directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof

2015-11-01

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

Ising antiferromagnet on the Archimedean lattices.

PubMed

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Ising antiferromagnet on the Archimedean lattices

NASA Astrophysics Data System (ADS)

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Ground-state magnetization of the Ising spin glass: A recursive numerical method and Chen-Ma scaling

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Chalangari, Fartash

2018-03-01

The ground-state properties of quasi-one-dimensional (Q1D) Ising spin glass are investigated using an exact numerical approach and analytical arguments. A set of coupled recursive equations for the ground-state energy are introduced and solved numerically. For various types of coupling distribution, we obtain accurate results for magnetization, particularly in the presence of a weak external magnetic field. We show that in the weak magnetic field limit, similar to the 1D model, magnetization exhibits a singular power-law behavior with divergent susceptibility. Remarkably, the spectrum of magnetic exponents is markedly different from that of the 1D system even in the case of two coupled chains. The magnetic exponent makes a crossover from being dependent on a distribution function to a constant value independent of distribution. We provide an analytic theory for these observations by extending the Chen-Ma argument to the Q1D case. We derive an analytical formula for the exponent which is in perfect agreement with the numerical results.

Critical behavior of the order-disorder phase transition in β -brass investigated by x-ray scattering

NASA Astrophysics Data System (ADS)

Madsen, A.; Als-Nielsen, J.; Hallmann, J.; Roth, T.; Lu, W.

2016-07-01

β -brass exhibits an archetypical example of an order-disorder transition with a critical behavior that was previously investigated by neutron scattering. The data were well described by the three-dimensional (3d) Ising model but the relatively crude experimental resolution prevented an in-depth examination of the single-length scaling hypothesis, a cornerstone in the theory of critical phenomena. With the development of synchrotron x-ray experiments, high-resolution data could be recorded and surprisingly it was found that the single-length scaling did not hold in most critical systems, possibly due to strain originating from surface defects and/or impurities. In this paper we demonstrate single-length critical behavior using high-resolution x-ray scattering in β -brass. The investigations confirm that β -brass behaves like a 3d Ising system over a wide range of length scales comprising correlated clusters of millions of atoms. To vary the surface sensitivity, experiments have been performed both in Bragg reflection and Laue transmission geometries but without any substantial differences observed in the scaling and critical behavior.

Defect-phase-dynamics approach to statistical domain-growth problem of clock models

NASA Technical Reports Server (NTRS)

Kawasaki, K.

1985-01-01

The growth of statistical domains in quenched Ising-like p-state clock models with p = 3 or more is investigated theoretically, reformulating the analysis of Ohta et al. (1982) in terms of a phase variable and studying the dynamics of defects introduced into the phase field when the phase variable becomes multivalued. The resulting defect/phase domain-growth equation is applied to the interpretation of Monte Carlo simulations in two dimensions (Kaski and Gunton, 1983; Grest and Srolovitz, 1984), and problems encountered in the analysis of related Potts models are discussed. In the two-dimensional case, the problem is essentially that of a purely dissipative Coulomb gas, with a sq rt t growth law complicated by vertex-pinning effects at small t.

Numerical tests of local scale invariance in ageing q-state Potts models

NASA Astrophysics Data System (ADS)

Lorenz, E.; Janke, W.

2007-01-01

Much effort has been spent over the last years to achieve a coherent theoretical description of ageing as a non-linear dynamics process. Long supposed to be a consequence of the slow dynamics of glassy systems only, ageing phenomena could also be identified in the phase-ordering kinetics of simple ferromagnets. As a phenomenological approach Henkel et al. developed a group of local scale transformations under which two-time autocorrelation and response functions should transform covariantly. This work is to extend previous numerical tests of the predicted scaling functions for the Ising model by Monte Carlo simulations of two-dimensional q-state Potts models with q=3 and 8, which, in equilibrium, undergo temperature-driven phase transitions of second and first order, respectively.

Quantum quenches in two spatial dimensions using chain array matrix product states

DOE PAGES

A. J. A. James; Konik, R.

2015-10-15

We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Tests of conformal field theory at the Yang-Lee singularity

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

Wydro, Tomasz; McCabe, John F.

2009-12-14

This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at the Yang-Lee edge singularity. Based on transfer matrix techniques, the single structure constant is evaluated at the Yang-Lee edge singularity. The results of both types of measurements are found to be fully consistent with the predictions for the (A{sub 4}, A{sub 1}) minimal conformal field theory, which was previously identified with this critical point.

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.

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

On discrete field theory properties of the dimer and Ising models and their conformal field theory limits

NASA Astrophysics Data System (ADS)

Kriz, Igor; Loebl, Martin; Somberg, Petr

2013-05-01

We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.

Optimal structure and parameter learning of Ising models

DOE PAGES

Lokhov, Andrey; Vuffray, Marc Denis; Misra, Sidhant; ...

2018-03-16

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, whichmore » is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.« less

Optimal structure and parameter learning of Ising models

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

Lokhov, Andrey; Vuffray, Marc Denis; Misra, Sidhant

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, whichmore » is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.« less

Magnetic properties of magnetic bilayer Kekulene structure: A Monte Carlo study

NASA Astrophysics Data System (ADS)

Jabar, A.; Masrour, R.

2018-06-01

In the present work, we have studied the magnetic properties of magnetic bilayer Kekulene structure with mixed spin-5/2 and spin-2 Ising model using Monte Carlo study. The magnetic phase diagrams of mixed spins Ising model have been given. The thermal total, partial magnetization and magnetic susceptibilities of the mixed spin-5/2 and spin-2 Ising model on a magnetic bilayer Kekulene structure are obtained. The transition temperature has been deduced. The effect of crystal field and exchange interactions on the this bilayers has been studied. The partial and total magnetic hysteresis cycles of the mixed spin-5/2 and spin-2 Ising model on a magnetic bilayer Kekulene structure have been given. The superparamagnetism behavior is observed in magnetic bilayer Kekulene structure. The magnetic coercive field decreases with increasing the exchange interactions between σ-σ and temperatures values and increases with increasing the absolute value of exchange interactions between σ-S. The multiple hysteresis behavior appears.

Quantum phase transition between cluster and antiferromagnetic states

NASA Astrophysics Data System (ADS)

Son, W.; Amico, L.; Fazio, R.; Hamma, A.; Pascazio, S.; Vedral, V.

2011-09-01

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state.

Characterizing quantum phase transition by teleportation

NASA Astrophysics Data System (ADS)

Wu, Meng-He; Ling, Yi; Shu, Fu-Wen; Gan, Wen-Cong

2018-04-01

In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence at the quantum critical point. The implications of this phenomenon and possible applications are also briefly discussed.

Entropy production in a Glauber–Ising irreversible model with dynamical competition

NASA Astrophysics Data System (ADS)

Barbosa, Oscar A.; Tomé, Tânia

2018-06-01

An out of equilibrium Glauber–Ising model, evolving in accordance with an irreversible and stochastic Markovian dynamics, is analyzed in order to improve our comprehension concerning critical behavior and phase transitions in nonequilibrium systems. Therefore, a lattice model ruled by the competition between two Glauber dynamics acting on interlaced square lattices is proposed. Previous results have shown how the entropy production provides information about irreversibility and criticality. Mean-field approximations and Monte Carlo simulations were used in the analysis. The results obtained here show a continuous phase transition, reflected in the entropy production as a logarithmic divergence of its derivative, which suggests a shared universality class with the irreversible models invariant under the symmetry operations of the Ising model.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Monte Carlo simulation of Ising models by multispin coding on a vector computer

NASA Astrophysics Data System (ADS)

Wansleben, Stephan; Zabolitzky, John G.; Kalle, Claus

1984-11-01

Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

NASA Astrophysics Data System (ADS)

Fabrizio, Michele

2018-06-01

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

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

Valentim, Alexandra; Rocha, Julio C. S.; Tsai, Shan-Ho

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, inmore » which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this diculty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.« less

Investigation of phase diagrams for cylindrical Ising nanotube using cellular automata

NASA Astrophysics Data System (ADS)

Astaraki, M.; Ghaemi, M.; Afzali, K.

2018-05-01

Recent developments in the field of applied nanoscience and nanotechnology have heightened the need for categorizing various characteristics of nanostructures. In this regard, this paper establishes a novel method to investigate magnetic properties (phase diagram and spontaneous magnetization) of a cylindrical Ising nanotube. Using a two-layer Ising model and the core-shell concept, the interactions within nanotube has been modelled. In the model, both ferromagnetic and antiferromagnetic cases have been considered. Furthermore, the effect of nanotube's length on the critical temperature is investigated. The model has been simulated using cellular automata approach and phase diagrams were constructed for different values of inter- and intra-layer couplings. For the antiferromagnetic case, the possibility of existence of compensation point is observed.

Critical Behavior of the Annealed Ising Model on Random Regular Graphs

NASA Astrophysics Data System (ADS)

Can, Van Hao

2017-11-01

In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121-161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by n^{3/4} converges to a specific random variable, with n the number of vertices of random regular graphs.

Precision islands in the Ising and O(N ) models

DOE PAGES

Kos, Filip; Poland, David; Simmons-Duffin, David; ...

2016-08-04

We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ϵ , λ σσϵ , λ ϵϵϵ ) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of thesemore » quantities to date.« less

Block voter model: Phase diagram and critical behavior

NASA Astrophysics Data System (ADS)

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

2011-11-01

We introduce and study the block voter model with noise on two-dimensional square lattices using Monte Carlo simulations and finite-size scaling techniques. The model is defined by an outflow dynamics where a central set of NPCS spins, here denoted by persuasive cluster spins (PCS), tries to influence the opinion of their neighboring counterparts. We consider the collective behavior of the entire system with varying PCS size. When NPCS>2, the system exhibits an order-disorder phase transition at a critical noise parameter qc which is a monotonically increasing function of the size of the persuasive cluster. We conclude that a larger PCS has more power of persuasion, when compared to a smaller one. It also seems that the resulting critical behavior is Ising-like independent of the range of interaction.

Orbital-selective Mott phases of a one-dimensional three-orbital Hubbard model studied using computational techniques

DOE PAGES

Liu, Guangkun; Kaushal, Nitin; Liu, Shaozhi; ...

2016-06-24

A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rincón et al., Phys. Rev. Lett. 112, 106405 (2014)]. In this paper we show that the constrained-path quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. In addition, we study a simplified version of themore » model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional density matrix renormalization group and determinant quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild fermion sign problems. Lastly, we conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean-field approximations.« less

Concurrence and fidelity of a Bose-Fermi mixture in a one-dimensional optical lattice.

PubMed

Ning, Wen-Qiang; Gu, Shi-Jian; Chen, Yu-Guang; Wu, Chang-Qin; Lin, Hai-Qing

2008-06-11

We study the ground-state fidelity and entanglement of a Bose-Fermi mixture loaded in a one-dimensional optical lattice. It is found that the fidelity is able to signal quantum phase transitions between the Luttinger liquid phase, the density-wave phase, and the phase separation state of the system, and the concurrence, as a measure of the entanglement, can be used to signal the transition between the density-wave phase and the Ising phase.

Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

NASA Astrophysics Data System (ADS)

Kim, Isaac H.

2011-05-01

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Wei, Bo-Bo

2018-04-01

In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and Rényi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.

Loop optimization for tensor network renormalization

NASA Astrophysics Data System (ADS)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Boson-mediated quantum spin simulators in transverse fields: X Y model and spin-boson entanglement

NASA Astrophysics Data System (ADS)

Wall, Michael L.; Safavi-Naini, Arghavan; Rey, Ana Maria

2017-01-01

The coupling of spins to long-wavelength bosonic modes is a prominent means to engineer long-range spin-spin interactions, and has been realized in a variety of platforms, such as atoms in optical cavities and trapped ions. To date, much of the experimental focus has been on the realization of long-range Ising models, but generalizations to other spin models are highly desirable. In this work, we explore a previously unappreciated connection between the realization of an X Y model by off-resonant driving of a single sideband of boson excitation (i.e., a single-beam Mølmer-Sørensen scheme) and a boson-mediated Ising simulator in the presence of a transverse field. In particular, we show that these two schemes have the same effective Hamiltonian in suitably defined rotating frames, and analyze the emergent effective X Y spin model through a truncated Magnus series and numerical simulations. In addition to X Y spin-spin interactions that can be nonperturbatively renormalized from the naive Ising spin-spin coupling constants, we find an effective transverse field that is dependent on the thermal energy of the bosons, as well as other spin-boson couplings that cause spin-boson entanglement not to vanish at any time. In the case of a boson-mediated Ising simulator with transverse field, we discuss the crossover from transverse field Ising-like to X Y -like spin behavior as a function of field strength.

The third law of thermodynamics and the fractional entropies

NASA Astrophysics Data System (ADS)

Baris Bagci, G.

2016-08-01

We consider the fractal calculus based Ubriaco and Machado entropies and investigate whether they conform to the third law of thermodynamics. The Ubriaco entropy satisfies the third law of thermodynamics in the interval 0 < q ≤ 1 exactly where it is also thermodynamically stable. The Machado entropy, on the other hand, yields diverging inverse temperature in the region 0 < q ≤ 1, albeit with non-vanishing negative entropy values. Therefore, despite the divergent inverse temperature behavior, the Machado entropy fails the third law of thermodynamics. We also show that the aforementioned results are also supported by the one-dimensional Ising model with no external field.

Herding, minority game, market clearing and efficient markets in a simple spin model framework

NASA Astrophysics Data System (ADS)

Kristoufek, Ladislav; Vosvrda, Miloslav

2018-01-01

We present a novel approach towards the financial Ising model. Most studies utilize the model to find settings which generate returns closely mimicking the financial stylized facts such as fat tails, volatility clustering and persistence, and others. We tackle the model utility from the other side and look for the combination of parameters which yields return dynamics of the efficient market in the view of the efficient market hypothesis. Working with the Ising model, we are able to present nicely interpretable results as the model is based on only two parameters. Apart from showing the results of our simulation study, we offer a new interpretation of the Ising model parameters via inverse temperature and entropy. We show that in fact market frictions (to a certain level) and herding behavior of the market participants do not go against market efficiency but what is more, they are needed for the markets to be efficient.

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)

The structural phase diagram and oxygen equilibrium partial pressure of YBa 2Cu 3O 6+ x studied by neutron powder diffraction and gas volumetry

NASA Astrophysics Data System (ADS)

Andersen, N. H.; Lebech, B.; Poulsen, H. F.

1990-12-01

An experimental technique based on neutron powder diffraction and gas volumetry is presented and used to study the structural phase diagram of YBa 2Cu 3O 6+ x under equilibrium conditions in an extended part of ( x, T)-phase (0.15< x<0.92 and 25° C< T<725°C). Our experimental observations lend strong support to a recent two-dimensional anisotropic next-nearest-neighbour Ising model calculation (the ASYNNNI model) of the basal plane oxygen ordering based of first principle interaction parameters. Simultaneous measurements of the oxygen equilibrium partial pressure show anomalies, one of which proves the thermodynamic stability of the orthorhombic OII double cell structure. Striking similarity with predictions of recent model calculations support that another anomaly may be interpreted to result from local one-dimensional fluctuations in the distribution of oxygen atoms in the basal plane of tetragonal YBCO. Our pressure data also indicate that x=0.92 is a maximum obtainable oxygen concentration for oxygen pressures below 760 Torr.

Quasi-one-dimensional magnetism in MnxFe1-xNb2O6 compounds: From Heisenberg to Ising chains

NASA Astrophysics Data System (ADS)

Hneda, M. L.; Oliveira Neto, S. R.; da Cunha, J. B. M.; Gusmão, M. A.; Isnard, O.

2018-06-01

A series of MnxFe1-xNb2O6 compounds (0 ⩽ x ⩽ 1) is investigated by both X-ray and neutron powder diffraction, as well as specific-heat and magnetic measurements. The samples present orthorhombic Pbcn crystal symmetry, and exhibit weakly coupled magnetic chains. These chains are of Heisenberg type (weak anisotropy) on the Mn-rich side, and Ising-like (strong anisotropy) on the Fe-rich side. Except for 100% Fe (x = 0) , which has weakly-interacting ferromagnetic Ising chains, a negative Curie-Weiss temperature is obtained from the magnetic susceptibility, indicating dominant antiferromagnetic interactions. At the lowest probed temperature, T = 1.5K , true long-range magnetic order is only observed for x = 1 , 0.8, and 0. Although the ordering is globally antiferromagnetic in all cases, the first two are characterized by a two-sublattice structure with propagation vector k = (0, 0, 0) , while the latter presents alternatingly oriented ferromagnetic chains described by k = (0,1/2, 0) . For other compositions, short-range magnetic correlations are extracted from diffuse neutron-scattering data.

Heat conduction in one-dimensional aperiodic quantum Ising chains.

PubMed

Li, Wenjuan; Tong, Peiqing

2011-03-01

The heat conductivity of nonperiodic quantum Ising chains whose ends are connected with heat baths at different temperatures are studied numerically by solving the Lindblad master equation. The chains are subjected to a uniform transverse field h, while the exchange coupling J{m} between the nearest-neighbor spins takes the two values J{A} and J{B} arranged in Fibonacci, generalized Fibonacci, Thue-Morse, and period-doubling sequences. We calculate the energy-density profile and energy current of the resulting nonequilibrium steady states to study the heat-conducting behavior of finite but large systems. Although these nonperiodic quantum Ising chains are integrable, it is clearly found that energy gradients exist in all chains and the energy currents appear to scale as the system size ~N{α}. By increasing the ratio of couplings, the exponent α can be modulated from α > -1 to α < -1 corresponding to the nontrivial transition from the abnormal heat transport to the heat insulator. The influences of the temperature gradient and the magnetic field to heat conduction have also been discussed.

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit

DOE PAGES

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén; ...

2017-06-07

Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes thismore » restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI 3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phases, showcasing the hallmark thickness dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena.« less

Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit

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

Huang, Bevin; Clark, Genevieve; Navarro-Moratalla, Efrén

Since the celebrated discovery of graphene, the family of two-dimensional (2D) materials has grown to encompass a broad range of electronic properties. Recent additions include spin-valley coupled semiconductors, Ising superconductors that can be tuned into a quantum metal, possible Mott insulators with tunable charge-density waves, and topological semi-metals with edge transport. Despite this progress, there is still no 2D crystal with intrinsic magnetism, which would be useful for many technologies such as sensing, information, and data storage. Theoretically, magnetic order is prohibited in the 2D isotropic Heisenberg model at finite temperatures by the Mermin-Wagner theorem. However, magnetic anisotropy removes thismore » restriction and enables, for instance, the occurrence of 2D Ising ferromagnetism. Here, we use magneto-optical Kerr effect (MOKE) microscopy to demonstrate that monolayer chromium triiodide (CrI 3) is an Ising ferromagnet with out-of-plane spin orientation. Its Curie temperature of 45 K is only slightly lower than the 61 K of the bulk crystal, consistent with a weak interlayer coupling. Moreover, our studies suggest a layer-dependent magnetic phases, showcasing the hallmark thickness dependent physical properties typical of van der Waals crystals. Remarkably, bilayer CrI3 displays suppressed magnetization with a metamagnetic effect, while in trilayer the interlayer ferromagnetism observed in the bulk crystal is restored. Our work creates opportunities for studying magnetism by harnessing the unique features of atomically-thin materials, such as electrical control for realizing magnetoelectronics, and van der Waals engineering for novel interface phenomena.« less

Tricriticality in the q-neighbor Ising model on a partially duplex clique.

PubMed

Chmiel, Anna; Sienkiewicz, Julian; Sznajd-Weron, Katarzyna

2017-12-01

We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r^{*}(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears.

Anisotropy of stress correlation in two-dimensional liquids and a pseudospin model

DOE PAGES

Wu, Bin; Iwashita, Takuya; Egami, Takeshi

2015-11-04

Liquids are condensed matter in which atoms are strongly correlated in position and momentum. The atomic pair density function (PDF) is used often in describing such correlation. However, elucidation of many properties requires higher degrees of correlation than the pair correlation. For instance, viscosity depends upon the stress correlations in space and time. We examine the cross correlation between the stress correlation at the atomic level and the PDF for two-dimensional liquids. We introduce the concept of the stress-resolved pair distribution function (SRPDF) that uses the sign of atomic-level stress as a selection rule to include particles from density correlations.more » The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. Lastly, we further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions.« less

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Ising model versus normal form game

NASA Astrophysics Data System (ADS)

Galam, Serge; Walliser, Bernard

2010-02-01

The 2-spin Ising model in statistical mechanics and the 2×2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no longer when Pareto optimum considerations are introduced as in the prisoner’s dilemma. This gap can nevertheless be filled by adding a new coupling term to the Ising model, even if that term has up to now no physical meaning. An individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2×2 game. Using this one-to-one mapping new perspectives for future research in both fields can be envisioned.

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

An analysis of intergroup rivalry using Ising model and reinforcement learning

NASA Astrophysics Data System (ADS)

Zhao, Feng-Fei; Qin, Zheng; Shao, Zhuo

2014-01-01

Modeling of intergroup rivalry can help us better understand economic competitions, political elections and other similar activities. The result of intergroup rivalry depends on the co-evolution of individual behavior within one group and the impact from the rival group. In this paper, we model the rivalry behavior using Ising model. Different from other simulation studies using Ising model, the evolution rules of each individual in our model are not static, but have the ability to learn from historical experience using reinforcement learning technique, which makes the simulation more close to real human behavior. We studied the phase transition in intergroup rivalry and focused on the impact of the degree of social freedom, the personality of group members and the social experience of individuals. The results of computer simulation show that a society with a low degree of social freedom and highly educated, experienced individuals is more likely to be one-sided in intergroup rivalry.

Cosmic ray composition investigations using ICE/ISEE-3

NASA Technical Reports Server (NTRS)

Wiedenbeck, Mark E.

1992-01-01

The analysis of data from the high energy cosmic experiment on ISEE-3 and associated modeling and interpretation activities are discussed. The ISEE-3 payload included two instruments capable of measuring the composition of heavy cosmic rays. The designs of these two instruments incorporated innovations which made it possible, for the first time, to measure isotopic as well as the chemical composition for a wide range of elements. As the result of the demonstrations by these two instruments of the capability to resolve individual cosmic ray isotopes, a new generation of detectors was developed using very similar designs, but having improved reliability and increased sensitive area. The composition measurements which were obtained from the ISEE-3 experiment are summarized.

Stability of the quantum Sherrington-Kirkpatrick spin glass model

NASA Astrophysics Data System (ADS)

Young, A. P.

2017-09-01

I study in detail the quantum Sherrington-Kirkpatrick (SK) model, i.e., the infinite-range Ising spin glass in a transverse field, by solving numerically the effective one-dimensional model that the quantum SK model can be mapped to in the thermodynamic limit. I find that the replica symmetric solution is unstable down to zero temperature, in contrast to some previous claims, and so there is not only a line of transitions in the (longitudinal) field-temperature plane (the de Almeida-Thouless, AT, line) where replica symmetry is broken, but also a quantum de Almeida-Thouless (QuAT) line in the transverse field-longitudinal field plane at T =0 . If the QuAT line also occurs in models with short-range interactions its presence might affect the performance of quantum annealers when solving spin glass-type problems with a bias (i.e., magnetic field).

Dynamical quantum phase transitions in extended transverse Ising models

NASA Astrophysics Data System (ADS)

Bhattacharjee, Sourav; Dutta, Amit

2018-04-01

We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with an additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model, where different quantum phases are characterized by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate, thereby leading to a single critical time scale for a given sector of Fisher zeros.

Model parameter learning using Kullback-Leibler divergence

NASA Astrophysics Data System (ADS)

Lin, Chungwei; Marks, Tim K.; Pajovic, Milutin; Watanabe, Shinji; Tung, Chih-kuan

2018-02-01

In this paper, we address the following problem: For a given set of spin configurations whose probability distribution is of the Boltzmann type, how do we determine the model coupling parameters? We demonstrate that directly minimizing the Kullback-Leibler divergence is an efficient method. We test this method against the Ising and XY models on the one-dimensional (1D) and two-dimensional (2D) lattices, and provide two estimators to quantify the model quality. We apply this method to two types of problems. First, we apply it to the real-space renormalization group (RG). We find that the obtained RG flow is sufficiently good for determining the phase boundary (within 1% of the exact result) and the critical point, but not accurate enough for critical exponents. The proposed method provides a simple way to numerically estimate amplitudes of the interactions typically truncated in the real-space RG procedure. Second, we apply this method to the dynamical system composed of self-propelled particles, where we extract the parameter of a statistical model (a generalized XY model) from a dynamical system described by the Viscek model. We are able to obtain reasonable coupling values corresponding to different noise strengths of the Viscek model. Our method is thus able to provide quantitative analysis of dynamical systems composed of self-propelled particles.

Field induced phase transition in layered honeycomb spin system α-RuCl3 studied by thermal conductivity

NASA Astrophysics Data System (ADS)

Leahy, Ian; Bornstein, Alex; Choi, Kwang-Yong; Lee, Minhyea

α -RuCl3, a quasi -two-dimensional honeycomb lattice is known to be a candidate material to realize the Heisenberg-Kitaev spin model of a highly anisotropic bond-dependent exchange interaction. We investigate in-plane thermal conductivity (κ) as a function of temperature (T) and in-plane applied field (H). At H = 0 , the onset of a strong increase in κ marks the spontaneous long range ordering temperature, Tc = 6 . 5 K , corresponding to ``zigzag'' antiferromagnetic ordering. A broad peak appearing below Tc in κ was found to be suppressed significantly as H increases up to ~ 7 T , implying the system undergoes a field-induced transition from ordered to a new spin-disordered state analogous to the transverse-field Ising model. Further increasing H above 7 . 1 T , the large field seems to begin polarizing spins thus increasing the phonon mean free path, resulting in a significant rise in κ. This tendency is clearly shown in the field dependence of κ below Tc, which has a pronounced minimum at Hmin = 7 . 1 T . We will discuss our scaling analysis to characterize this field-induced phase transition and compare to the transverse-field Ising spin system. Work at the University of Colorado was supported by the US DOE Basic Energy Sciences under Award No. DE-SC0006888.

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.

A flower-like Ising model. Thermodynamic properties

NASA Astrophysics Data System (ADS)

Mejdani, R.; Ifti, M.

1995-03-01

We consider a flower-like Ising model, in which there are some additional bonds (in the “flower-core”) compared to a pure Ising chain. To understand the behaviour of this system and particularly the competition between ferromagnetic (usual) bonds along the chain and antiferromagnetic (additional) bonds across the chain, we study analytically and iteratively the main thermodynamic quantities. Very interesting is, in the zero-field and zero-temperature limit, the behaviour of the magnetization and the susceptibility, closely related to the ground state configurations and their degeneracies. This degeneracy explains the existence of non-zero entropy at zero temperature, in our results. Also, this model could be useful for the experimental investigations in studying the saturation curves for the enzyme kinetics or the melting curves for DNA-denaturation in some flower-like configurations.

Nonlinear spin susceptibility in topological insulators

NASA Astrophysics Data System (ADS)

Shiranzaei, Mahroo; Fransson, Jonas; Cheraghchi, Hosein; Parhizgar, Fariborz

2018-05-01

We revise the theory of the indirect exchange interaction between magnetic impurities beyond the linear response theory to establish the effect of impurity resonances in the surface states of a three-dimensional topological insulator. The interaction is composed of isotropic Heisenberg, anisotropic Ising, and Dzyaloshinskii-Moriya types of couplings. We find that all three contributions are finite at the Dirac point, which is in stark contrast to the linear response theory which predicts a vanishing Dzyaloshinskii-Moriya-type contribution. We show that the spin-independent component of the impurity scattering can generate large values of the Dzyaloshinskii-Moriya-type coupling in comparison with the Heisenberg and Ising types of couplings, while these latter contributions drastically reduce in magnitude and undergo sign changes. As a result, both collinear and noncollinear configurations are allowed magnetic configurations of the impurities.

Institute for Science and Engineering Simulation (ISES)

DTIC Science & Technology

2015-12-18

performance and other functionalities such as electrical , magnetic, optical, thermal, biological, chemical, and so forth. Structural integrity...transmission electron microscopy (HRSTEM) and three-dimensional atom probe (3DAP) tomography , the true atomic scale structure and change in chemical...atom probe tomography (3DAP) techniques, has permitted characterizing and quantifying the multimodal size distribution of different generations of γ

Nanothermodynamics Applied to Thermal Processes in Heterogeneous Materials

DTIC Science & Technology

2012-08-03

models agree favorably with a wide range of measurements of local thermal and dynamic properties. Progress in understanding basic thermodynamic...Monte- Carlo (MC) simulations of the Ising model .7 The solid black lines in Fig. 4 show results using the uncorrected (Metropolis) algorithm on the...parameter g=0.5 (green, dash-dot), g=1 (black, solid ), and g=2 (blue, dash-dot-dot). Note the failure of the standard Ising model (g=0) to match

Indentation size effects in single crystal copper as revealed by synchrotron x-ray microdiffraction

NASA Astrophysics Data System (ADS)

Feng, G.; Budiman, A. S.; Nix, W. D.; Tamura, N.; Patel, J. R.

2008-08-01

For a Cu single crystal, we find that indentation hardness increases with decreasing indentation depth, a phenomenon widely observed before and called the indentation size effect (ISE). To understand the underlying mechanism, we measure the lattice rotations in indentations of different sizes using white beam x-ray microdiffraction (μXRD); the indentation-induced lattice rotations are directly measured by the streaking of x-ray Laue spots associated with the indentations. The magnitude of the lattice rotations is found to be independent of indentation size, which is consistent with the basic tenets of the ISE model. Using the μXRD data together with an ISE model, we can estimate the effective radius of the indentation plastic zone, and the estimate is consistent with the value predicted by a finite element analysis. Using these results, an estimate of the average dislocation densities within the plastic zones has been made; the findings are consistent with the ISE arising from a dependence of the dislocation density on the depth of indentation.

Performance evaluation of coherent Ising machines against classical neural networks

NASA Astrophysics Data System (ADS)

Haribara, Yoshitaka; Ishikawa, Hitoshi; Utsunomiya, Shoko; Aihara, Kazuyuki; Yamamoto, Yoshihisa

2017-12-01

The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

Ising Model on Tangled Chain, Some Thermodynamic Properties

NASA Astrophysics Data System (ADS)

Mejdani, R.

1996-09-01

In this paper we consider an Ising model on tangled chain, where some additional bonds compared to a pure Ising chain are presented. To understand the behavior of this system and the competition between ferromagnetic bonds J along the chain and antiferromagnetic bonds J' across the chain, we have studied in detail analytically and iteratively some of the thermodynamic quantities. Particularly interesting is, in the zero-field and zero-temperature limit, the behavior of the magnetization and the susceptibility closely related to the ground-state configurations and their degeneracies. This degeneracy, presented at the condition J' ≤ -J between J and J', explains, also, the existence of nonzero entropy at zero temperature. This model applied as a lattice gas model defined on a tangled chain could be also useful for the experimental investigations in studying the saturation curves for the enzyme kinetics or the melting curves for DNA-denaturation.

Dynamic Transition and Resonance in Coupled Oscillators Under Symmetry-Breaking Fields

NASA Astrophysics Data System (ADS)

Choi, J.; Choi, M. Y.; Chung, M. S.; Yoon, B.-G.

2013-06-01

We investigate numerically the dynamic properties of a system of globally coupled oscillators driven by periodic symmetry-breaking fields in the presence of noise. The phase distribution of the oscillators is computed and a dynamic transition is disclosed. It is further found that the stochastic resonance is closely related to the behavior of the dynamic order parameter, which is in turn explained by the formation of a bi-cluster in the system. Here noise tends to symmetrize the motion of the oscillators, facilitating the bi-cluster formation. The observed resonance appears to be of the same class as the resonance present in the two-dimensional Ising model under oscillating fields.

Droplet states in quantum XXZ spin systems on general graphs

NASA Astrophysics Data System (ADS)

Fischbacher, C.; Stolz, G.

2018-05-01

We study XXZ spin systems on general graphs. In particular, we describe the formation of droplet states near the bottom of the spectrum in the Ising phase of the model, where the Z-term dominates the XX-term. As key tools, we use particle number conservation of XXZ systems and symmetric products of graphs with their associated adjacency matrices and Laplacians. Of particular interest to us are strips and multi-dimensional Euclidean lattices, for which we discuss the existence of spectral gaps above the droplet regime. We also prove a Combes-Thomas bound which shows that the eigenstates in the droplet regime are exponentially small perturbations of strict (classical) droplets.

Local and nonlocal order parameters in the Kitaev chain

NASA Astrophysics Data System (ADS)

Chitov, Gennady Y.

2018-02-01

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices, we infer the two-dimensional Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

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.

Effective-field renormalization-group method for Ising systems

NASA Astrophysics Data System (ADS)

Fittipaldi, I. P.; De Albuquerque, D. F.

1992-02-01

A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Finitized conformal spectrum of the Ising model on the cylinder and torus

NASA Astrophysics Data System (ADS)

O'Brien, David L.; Pearce, Paul A.; Ole Warnaar, S.

1996-02-01

The spectrum of the critical Ising model on a lattice with cylindrical and toroidal boundary conditions is calculated by commuting transfer matrix methods. Using a simple truncation procedure, we obtain the natural finitizations of the conformal spectra recently proposed by Melzer. These finitizations imply polynomial identities which in the large lattice limit give rise to the Rogers-Ramanujan identities for the c = {1}/{2} Virasoro characters.

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

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

Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models

NASA Astrophysics Data System (ADS)

Mitchell, S. J.; Landau, D. P.

2006-03-01

Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic (s=1/2) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems (512^2) and long times (10^ 6 MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of 1/3 [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.Supported by the NSF.[1] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, second ed. (Cambridge University Press, New York, 2005).[2] J. Amar, F. Sullivan, and R.D. Mountain, Phys. Rev. B 37, 196 (1988).

ISING MODEL OF CHORIOCAPILLARIS FLOW.

PubMed

Spaide, Richard F

2018-01-01

To develop a mathematical model of local blood flow in the choriocapillaris using an Ising model. A JavaScript Ising model was used to create images that emulated the development of signal voids as would be seen in optical coherence tomography angiography of the choriocapillaris. The model was produced by holding the temperature near criticality and varying the field strength. Individual frames were evaluated, and a movie video was created to show the hypothetical development of flow-related signal voids over a lifetime. Much the same as actual choriocapillaris images in humans, the model of flow-related signal voids followed a power-law distribution. The slope and intercept both decreased with age, as is seen in human subjects. This model is a working hypothesis, and as such can help predict system characteristics, evaluate conclusions drawn from studies, suggest new research questions, and provide a way of obtaining an estimate of behavior in which experimental data are not yet available. It may be possible to understand choriocapillaris blood flow in health and disease states by determining by observing deviations from an expected model.

Yang-Baxter and other relations for free-fermion and Ising models

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

Davies, B.

1987-02-01

Eight-vertex, free fermion, and Ising models are formulated using a convention that emphasizes the algebra of the local transition operators that arise in the quantum inverse method. Equivalent classes of models, are investigated, with particular emphasis on the role of the star-triangle relations. Using these results, a natural and symmetrical parametrization is introduced and Yang-Baxter relations are constructed in an elementary way. The paper concludes with a consideration of duality, which links the present work to a recent paper of Baxter on the free fermion model.

Microscopic Spin Model for the STOCK Market with Attractor Bubbling on Regular and Small-World Lattices

NASA Astrophysics Data System (ADS)

Krawiecki, A.

A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.

Magnetic structure and dispersion relation of the S = 1 2 quasi-one-dimensional Ising-like antiferromagnet BaCo 2 V 2 O 8 in a transverse magnetic field

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

Matsuda, M.; Onishi, H.; Okutani, A.

Here, BaCo 2V 2O 8 consists of Co chains in which a Co 2+ ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo 2V 2O 8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis.more » We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 XXZ antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.« less

Two-dimensional Magnetism in Arrays of Superconducting Rings

NASA Astrophysics Data System (ADS)

Reich, Daniel H.

1996-03-01

An array of superconducting rings in an applied field corresponding to a flux of Φ0 /2 per ring behaves like a 2D Ising antiferromagnet. Each ring has two energetically equivalent states with equal and opposite magnetic moments due to fluxoid quantization, and the dipolar coupling between rings favors antiparallel alignment of the moments. Using SQUID magnetometry and scanning Hall probe microscopy, we have studied the dynamics and magnetic configurations of micron-size aluminum rings on square, triangular, honeycomb, and kagomé lattices. We have found that there are significant antiferromagnetic correlations between rings, and that effects of geometrical frustration can be observed on the triangular and kagomé lattices. Long range correlations on the other lattices are suppressed by the analog of spin freezing that locks the rings in metastable states at low temperatures, and by quenched disorder due to imperfections in the fabrication. This disorder produces a roughly 1% variation in the rings' areas, which translates into an effective random field on the spins. The ring arrays are thus an extremely good realization of the 2D random-field Ising model. (Performed in collaboration with D. Davidović, S. Kumar, J. Siegel, S. B. Field, R. C. Tiberio, R. Hey, and K. Ploog.) (Supported by NSF grants DMR-9222541, and DMR-9357518, and by the David and Lucile Packard Foundation.)

Magnetic structure and dispersion relation of the S = 1 2 quasi-one-dimensional Ising-like antiferromagnet BaCo 2 V 2 O 8 in a transverse magnetic field

DOE PAGES

Matsuda, M.; Onishi, H.; Okutani, A.; ...

2017-07-25

Here, BaCo 2V 2O 8 consists of Co chains in which a Co 2+ ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo 2V 2O 8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis.more » We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 XXZ antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.« less

Magnetic structure and dispersion relation of the S =1/2 quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8 in a transverse magnetic field

NASA Astrophysics Data System (ADS)

Matsuda, M.; Onishi, H.; Okutani, A.; Ma, J.; Agrawal, H.; Hong, T.; Pajerowski, D. M.; Copley, J. R. D.; Okunishi, K.; Mori, M.; Kimura, S.; Hagiwara, M.

2017-07-01

BaCo2V2O8 consists of Co chains in which a Co2 + ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo2V2O8 in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis. We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 X X Z antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations.

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.

Quantum-information approach to the Ising model: Entanglement in chains of qubits

NASA Astrophysics Data System (ADS)

Štelmachovič, Peter; Bužek, Vladimír

2004-09-01

Simple physical interactions between spin- 1/2 particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin- 1/2 particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin- 1/2 particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter λ has a maximum around the point λ=1 , and it monotonically decreases for large values of λ . We prove that in the limit λ→∞ this state is locally unitary equivalent to an N -partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the X -state). This X -state exhibits the “extreme” entanglement in a sense that an arbitrary subset A of k⩽n qubits in the Ising chain composed of N=2n+1 qubits is maximally entangled with the remaining qubits (set B ) in the chain. In addition, we prove that by performing a local operation just on the subset B , one can transform the X -state into a direct product of k singlets shared by the parties A and B . This property of the X -state can be utilized for new secure multipartite communication protocols.

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

DOE PAGES

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen; ...

2017-12-29

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

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

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic XXZ spin-1/2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic eld. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [Phys. Rev. B 81, 144419 (2010)]. We also con rm the prevalence of the Nz Neel Ising order in the regime of comparable DM and magnetic field magnitudes.

A Q-Ising model application for linear-time image segmentation

NASA Astrophysics Data System (ADS)

Bentrem, Frank W.

2010-10-01

A computational method is presented which efficiently segments digital grayscale images by directly applying the Q-state Ising (or Potts) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems ( i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to partitioning the system into regions of four classes of magnetism. This direct Potts segmentation technique is demonstrated on photographic, medical, and acoustic images.

Topological entanglement entropy with a twist.

PubMed

Brown, Benjamin J; Bartlett, Stephen D; Doherty, Andrew C; Barrett, Sean D

2013-11-27

Defects in topologically ordered models have interesting properties that are reminiscent of the anyonic excitations of the models themselves. For example, dislocations in the toric code model are known as twists and possess properties that are analogous to Ising anyons. We strengthen this analogy by using the topological entanglement entropy as a diagnostic tool to identify properties of both defects and excitations in the toric code. Specifically, we show, through explicit calculation, that the toric code model including twists and dyon excitations has the same quantum dimensions, the same total quantum dimension, and the same fusion rules as an Ising anyon model.

Different as night and day: Patterns of isolated seizures, clusters, and status epilepticus.

PubMed

Goldenholz, Daniel M; Rakesh, Kshitiz; Kapur, Kush; Gaínza-Lein, Marina; Hodgeman, Ryan; Moss, Robert; Theodore, William H; Loddenkemper, Tobias

2018-05-01

Using approximations based on presumed U.S. time zones, we characterized day and nighttime seizure patterns in a patient-reported database, Seizure Tracker. A total of 632 995 seizures (9698 patients) were classified into 4 categories: isolated seizure event (ISE), cluster without status epilepticus (CWOS), cluster including status epilepticus (CIS), and status epilepticus (SE). We used a multinomial mixed-effects logistic regression model to calculate odds ratios (ORs) to determine night/day ratios for the difference between seizure patterns: ISE versus SE, ISE versus CWOS, ISE versus CIS, and CWOS versus CIS. Ranges of OR values were reported across cluster definitions. In adults, ISE was more likely at night compared to CWOS (OR = 1.49, 95% adjusted confidence interval [CI] = 1.36-1.63) and to CIS (OR = 1.61, 95% adjusted CI = 1.34-1.88). The ORs for ISE versus SE and CWOS versus SE were not significantly different regardless of cluster definition. In children, ISE was less likely at night compared to SE (OR = 0.85, 95% adjusted CI = 0.79-0.91). ISE was more likely at night compared to CWOS (OR = 1.35, 95% adjusted CI = 1.26-1.44) and CIS (OR = 1.65, 95% adjusted CI = 1.44-1.86). CWOS was more likely during the night compared to CIS (OR = 1.22, 95% adjusted CI = 1.05-1.39). With the exception of SE in children, our data suggest that more severe patterns favor daytime. This suggests distinct day/night preferences for different seizure patterns in children and adults. Wiley Periodicals, Inc. © 2018 International League Against Epilepsy.

Ibervillea sonorae (Cucurbitaceae) induces the glucose uptake in human adipocytes by activating a PI3K-independent pathway.

PubMed

Zapata-Bustos, Rocio; Alonso-Castro, Angel Josabad; Gómez-Sánchez, Maricela; Salazar-Olivo, Luis A

2014-03-28

Ibervillea sonorae (S. Watson) Greene (Cucurbitaceae), a plant used for the empirical treatment of type 2 diabetes in México, exerts antidiabetic effects on animal models but its mechanism of action remains unknown. The aim of this study is to investigate the antidiabetic mechanism of an Ibervillea sonorae aqueous extract (ISE). Non-toxic ISE concentrations were assayed on the glucose uptake by insulin-sensitive and insulin-resistant murine and human cultured adipocytes, both in the absence or the presence of insulin signaling pathway inhibitors, and on murine and human adipogenesis. Chemical composition of ISE was examined by spectrophotometric and HPLC techniques. ISE stimulated the 2-NBDGlucose uptake by mature adipocytes in a concentration-dependent manner. ISE 50 µg/ml induced the 2-NBDG uptake in insulin-sensitive 3T3-F442A, 3T3-L1 and human adipocytes by 100%, 63% and 33%, compared to insulin control. Inhibitors for the insulin receptor, PI3K, AKT and GLUT4 blocked the 2-NBDG uptake in murine cells, but human adipocytes were insensitive to the PI3K inhibitor Wortmannin. ISE 50 µg/ml also stimulated the 2-NBDG uptake in insulin-resistant adipocytes by 117% (3T3-F442A), 83% (3T3-L1) and 48% (human). ISE induced 3T3-F442A adipogenesis but lacked proadipogenic effects on 3T3-L1 and human preadipocytes. Chemical analyses showed the presence of phenolics in ISE, mainly an appreciable concentration of gallic acid. Ibervillea sonorae exerts its antidiabetic properties by means of hydrosoluble compounds stimulating the glucose uptake in human preadipocytes by a PI3K-independent pathway and without proadipogenic effects. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Data compressor designed to improve recognition of magnetic phases

NASA Astrophysics Data System (ADS)

Vogel, E. E.; Saravia, G.; Cortez, L. V.

2012-02-01

Data compressors available in the web have been used to determine magnetic phases for two-dimensional (2D) systems [E. Vogel, G. Saravia, F. Bachmann, B. Fierro, J. Fischer, Phase transitions in Edwards-Anderson model by means of information theory, Physica A 388 2009 4075-4082]. In the present work, we push this line forward along four different directions. First, the compressor itself: we design a new data compressor, named wlzip, optimized for the recognition of information having physical (or scientific) information instead of the random digital information usually compressed. Second, for the first time we extend the data compression analysis to the 3D Ising ferromagnetic model using wlzip. Third, we discuss the tuning possibilities of wlzip in terms of the number of digits considered in the compression to yield maximum definition; in this way, the transition temperature of both 2D and 3D Ising ferromagnets can be reported with very good resolution. Fourth, the extension of the time window through which the data file is actually compressed is also considered to get optimum accuracy. The paper is focused on the new compressor, its algorithm in general and the way to apply it. Advantages and disadvantages of wlzip are discussed. Toward the end, we mention other possible applications of this technique to recognize stable and unstable regimes in the evolution of variables in meteorology (such as pollution content or atmospheric pressure), biology (blood pressure) and econophysics (prices of the stock market).

Unconventional quantum antiferromagnetism with a fourfold symmetry breaking in a spin-1/2 Ising-Heisenberg pentagonal chain

NASA Astrophysics Data System (ADS)

Karľová, Katarína; Strečka, Jozef; Lyra, Marcelo L.

2018-03-01

The spin-1/2 Ising-Heisenberg pentagonal chain is investigated with use of the star-triangle transformation, which establishes a rigorous mapping equivalence with the effective spin-1/2 Ising zigzag ladder. The investigated model has a rich ground-state phase diagram including two spectacular quantum antiferromagnetic ground states with a fourfold broken symmetry. It is demonstrated that these long-period quantum ground states arise due to a competition between the effective next-nearest-neighbor and nearest-neighbor interactions of the corresponding spin-1/2 Ising zigzag ladder. The concurrence is used to quantify the bipartite entanglement between the nearest-neighbor Heisenberg spin pairs, which are quantum-mechanically entangled in two quantum ground states with or without spontaneously broken symmetry. The pair correlation functions between the nearest-neighbor Heisenberg spins as well as the next-nearest-neighbor and nearest-neighbor Ising spins were investigated with the aim to bring insight into how a relevant short-range order manifests itself at low enough temperatures. It is shown that the specific heat displays temperature dependencies with either one or two separate round maxima.

Maximally informative pairwise interactions in networks

PubMed Central

Fitzgerald, Jeffrey D.; Sharpee, Tatyana O.

2010-01-01

Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings between input signals and network states that allow the network to convey the maximal information about input signals drawn from a given distribution. This mapping also produces a set of linear equations for calculating the optimal Ising-model coupling constants, as well as geometric properties that indicate the applicability of the pairwise Ising model. We show that the optimal pairwise interactions are on average zero for Gaussian and uniformly distributed inputs, whereas they are nonzero for inputs approximating those in natural environments. These nonzero network interactions are predicted to increase in strength as the noise in the response functions of each network node increases. This approach also suggests ways for how interactions with unmeasured parts of the network can be inferred from the parameters of response functions for the measured network nodes. PMID:19905153

Improving Health Care Providers' Capacity for Self-Regulated Learning in Online Continuing Pharmacy Education: The Role of Internet Self-Efficacy.

PubMed

Chiu, Yen-Lin; Liang, Jyh-Chong; Mao, Pili Chih-Min; Tsai, Chin-Chung

2016-01-01

Although Internet-based learning is widely used to improve health professionals' knowledge and skills, the self-regulated learning (SRL) activities of online continuing education in pharmacy are seldom discussed. The main purpose of this study was to explore the relationships between pharmacists' Internet self-efficacy (ISE) and their SRL in online continuing education. A total of 164 in-service pharmacists in Taiwan were surveyed with the Internet Self-Efficacy Survey, including basic ISE (B-ISE), advanced ISE (A-ISE) and professional ISE (P-ISE), as well as the Self-Regulated Learning Questionnaire consisting of preparatory SRL (P-SRL) and enactment SRL (E-SRL). Results of a 1-by-3 (educational levels: junior college versus bachelor versus master) analysis of variance and a 1-by-4 (institutions: community-based versus hospital versus clinic versus company) analysis of variance revealed that there were differences in ISE and SRL among different education levels and working institutions. The hierarchical regression analyses indicated that B-ISE and P-ISE were significant predictors of P-SRL, whereas P-ISE was a critical predictor of E-SRL. Moreover, the interaction of P-ISE × age was linked to E-SRL, implying that P-ISE has a stronger influence on E-SRL for older pharmacists than for younger pharmacists. However, the interactions between age and ISE (A-ISE, B-ISE, and P-ISE) were not related to P-SRL. This study highlighted the importance of ISE and age for increasing pharmacists' SRL in online continuing education.

Implicit and Explicit Self-Esteem in Current, Remitted, Recovered, and Comorbid Depression and Anxiety Disorders: The NESDA Study.

PubMed

van Tuijl, Lonneke A; Glashouwer, Klaske A; Bockting, Claudi L H; Tendeiro, Jorge N; Penninx, Brenda W J H; de Jong, Peter J

2016-01-01

Dual processing models of psychopathology emphasize the relevance of differentiating between deliberative self-evaluative processes (explicit self-esteem; ESE) and automatically-elicited affective self-associations (implicit self-esteem; ISE). It has been proposed that both low ESE and ISE would be involved in major depressive disorder (MDD) and anxiety disorders (AD). Further, it has been hypothesized that MDD and AD may result in a low ISE "scar" that may contribute to recurrence after remission. However, the available evidence provides no straightforward support for the relevance of low ISE in MDD/AD, and studies testing the relevance of discrepant SE even showed that especially high ISE combined with low ESE is predictive of the development of internalizing symptoms. However, these earlier findings have been limited by small sample sizes, poorly defined groups in terms of comorbidity and phase of the disorders, and by using inadequate indices of discrepant SE. Therefore, this study tested further the proposed role of ISE and discrepant SE in a large-scale study allowing for stricter differentiation between groups and phase of disorder. In the context of the Netherlands Study of Depression and Anxiety (NESDA), we selected participants with current MDD (n = 60), AD (n = 111), and comorbid MDD/AD (n = 71), remitted MDD (n = 41), AD (n = 29), and comorbid MDD/AD (n = 14), recovered MDD (n = 136) and AD (n = 98), and never MDD or AD controls (n = 382). The Implicit Association Test was used to index ISE and the Rosenberg Self-Esteem Scale indexed ESE. Controls reported higher ESE than all other groups, and current comorbid MDD/AD had lower ESE than all other clinical groups. ISE was only lower than controls in current comorbid AD/MDD. Discrepant self-esteem (difference between ISE and ESE) was not associated with disorder status once controlling for ESE. Cross-sectional design limits causal inferences. Findings suggest a prominent role for ESE in MDD and AD, while in comorbid MDD/AD negative self-evaluations are also present at the implicit level. There was no evidence to support the view that AD and MDD would result in a low ISE "scar".

Enhanced multi-protocol analysis via intelligent supervised embedding (EMPrAvISE): detecting prostate cancer on multi-parametric MRI

NASA Astrophysics Data System (ADS)

Viswanath, Satish; Bloch, B. Nicholas; Chappelow, Jonathan; Patel, Pratik; Rofsky, Neil; Lenkinski, Robert; Genega, Elizabeth; Madabhushi, Anant

2011-03-01

Currently, there is significant interest in developing methods for quantitative integration of multi-parametric (structural, functional) imaging data with the objective of building automated meta-classifiers to improve disease detection, diagnosis, and prognosis. Such techniques are required to address the differences in dimensionalities and scales of individual protocols, while deriving an integrated multi-parametric data representation which best captures all disease-pertinent information available. In this paper, we present a scheme called Enhanced Multi-Protocol Analysis via Intelligent Supervised Embedding (EMPrAvISE); a powerful, generalizable framework applicable to a variety of domains for multi-parametric data representation and fusion. Our scheme utilizes an ensemble of embeddings (via dimensionality reduction, DR); thereby exploiting the variance amongst multiple uncorrelated embeddings in a manner similar to ensemble classifier schemes (e.g. Bagging, Boosting). We apply this framework to the problem of prostate cancer (CaP) detection on 12 3 Tesla pre-operative in vivo multi-parametric (T2-weighted, Dynamic Contrast Enhanced, and Diffusion-weighted) magnetic resonance imaging (MRI) studies, in turn comprising a total of 39 2D planar MR images. We first align the different imaging protocols via automated image registration, followed by quantification of image attributes from individual protocols. Multiple embeddings are generated from the resultant high-dimensional feature space which are then combined intelligently to yield a single stable solution. Our scheme is employed in conjunction with graph embedding (for DR) and probabilistic boosting trees (PBTs) to detect CaP on multi-parametric MRI. Finally, a probabilistic pairwise Markov Random Field algorithm is used to apply spatial constraints to the result of the PBT classifier, yielding a per-voxel classification of CaP presence. Per-voxel evaluation of detection results against ground truth for CaP extent on MRI (obtained by spatially registering pre-operative MRI with available whole-mount histological specimens) reveals that EMPrAvISE yields a statistically significant improvement (AUC=0.77) over classifiers constructed from individual protocols (AUC=0.62, 0.62, 0.65, for T2w, DCE, DWI respectively) as well as one trained using multi-parametric feature concatenation (AUC=0.67).

Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets

NASA Astrophysics Data System (ADS)

Sornette, Didier; Zhou, Wei-Xing

2006-10-01

Following a long tradition of physicists who have noticed that the Ising model provides a general background to build realistic models of social interactions, we study a model of financial price dynamics resulting from the collective aggregate decisions of agents. This model incorporates imitation, the impact of external news and private information. It has the structure of a dynamical Ising model in which agents have two opinions (buy or sell) with coupling coefficients, which evolve in time with a memory of how past news have explained realized market returns. We study two versions of the model, which differ on how the agents interpret the predictive power of news. We show that the stylized facts of financial markets are reproduced only when agents are overconfident and mis-attribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the critical point. Our model exhibits a rich multifractal structure characterized by a continuous spectrum of exponents of the power law relaxation of endogenous bursts of volatility, in good agreement with previous analytical predictions obtained with the multifractal random walk model and with empirical facts.

Pitfalls in Prediction Modeling for Normal Tissue Toxicity in Radiation Therapy: An Illustration With the Individual Radiation Sensitivity and Mammary Carcinoma Risk Factor Investigation Cohorts

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

Mbah, Chamberlain, E-mail: chamberlain.mbah@ugent.be; Department of Mathematical Modeling, Statistics, and Bioinformatics, Faculty of Bioscience Engineering, Ghent University, Ghent; Thierens, Hubert

Purpose: To identify the main causes underlying the failure of prediction models for radiation therapy toxicity to replicate. Methods and Materials: Data were used from two German cohorts, Individual Radiation Sensitivity (ISE) (n=418) and Mammary Carcinoma Risk Factor Investigation (MARIE) (n=409), of breast cancer patients with similar characteristics and radiation therapy treatments. The toxicity endpoint chosen was telangiectasia. The LASSO (least absolute shrinkage and selection operator) logistic regression method was used to build a predictive model for a dichotomized endpoint (Radiation Therapy Oncology Group/European Organization for the Research and Treatment of Cancer score 0, 1, or ≥2). Internal areas undermore » the receiver operating characteristic curve (inAUCs) were calculated by a naïve approach whereby the training data (ISE) were also used for calculating the AUC. Cross-validation was also applied to calculate the AUC within the same cohort, a second type of inAUC. Internal AUCs from cross-validation were calculated within ISE and MARIE separately. Models trained on one dataset (ISE) were applied to a test dataset (MARIE) and AUCs calculated (exAUCs). Results: Internal AUCs from the naïve approach were generally larger than inAUCs from cross-validation owing to overfitting the training data. Internal AUCs from cross-validation were also generally larger than the exAUCs, reflecting heterogeneity in the predictors between cohorts. The best models with largest inAUCs from cross-validation within both cohorts had a number of common predictors: hypertension, normalized total boost, and presence of estrogen receptors. Surprisingly, the effect (coefficient in the prediction model) of hypertension on telangiectasia incidence was positive in ISE and negative in MARIE. Other predictors were also not common between the 2 cohorts, illustrating that overcoming overfitting does not solve the problem of replication failure of prediction models completely. Conclusions: Overfitting and cohort heterogeneity are the 2 main causes of replication failure of prediction models across cohorts. Cross-validation and similar techniques (eg, bootstrapping) cope with overfitting, but the development of validated predictive models for radiation therapy toxicity requires strategies that deal with cohort heterogeneity.« less

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

Field-Induced Magnetic Phase Transitions in a Triangular Lattice Antiferromagnet CuFeO 2 up to 14.5 T

NASA Astrophysics Data System (ADS)

Mitsuda, Setsuo; Mase, Motoshi; Prokes, K.; Kitazawa, Hideaki; Katori, H.

2000-11-01

Neutron diffraction studies on a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been performed under an applied magnetic field up to 14.5 T. The first-field-induced state was found to be not the commensurate 5-sublattice (↑↑↑↓↓) magnetic state but rather an incommensurate complex helical state reflecting the Heisenberg spin character of orbital singlet Fe3+ magnetic ions. In contrast, the second-field-induced state was found to be the 5-sublattice (↑↑↑↓↓) magnetic state predicted by the two-dimensional (2D) Ising spin TLA model with competing exchange interactions up to the 3rd neighbors.

Reconnection at the earth's magnetopause - Magnetic field observations and flux transfer events

NASA Technical Reports Server (NTRS)

Russell, C. T.

1984-01-01

Theoretical models of plasma acceleration by magnetic-field-line reconnection at the earth magnetopause and the high-resolution three-dimensional plasma measurements obtained with the ISEE satellites are compared and illustrated with diagrams, graphs, drawings, and histograms. The history of reconnection theory and the results of early satellite observations are summarized; the thickness of the magnetopause current layer is discussed; problems in analyzing the polarization of current-layer rotation are considered; and the flux-transfer events responsible for periods of patchy reconnection are characterized in detail. The need for further observations and refinements of the theory to explain the initiation of reconnection and identify the mechanism determining whether it is patchy or steady-state is indicated.

Dynamic Algorithms for Transition Matrix Generation

NASA Astrophysics Data System (ADS)

Yevick, David; Lee, Yong Hwan

The methods of [D. Yevick, Int. J. Mod. Phys. C, 1650041] for constructing transition matrices are applied to the two dimensional Ising model. Decreasing the system temperature during the acquisition of the matrix elements yields a reasonably precise specific heat curve for a 32x32 spin system for a limited number (50-100M) of realizations. If the system is instead evolved to first higher and then lower energies within a restricted interval that is steadily displaced in energy as the computation proceeds, a modification which permits backward displacements up to a certain lower bound for each forward step ensures acceptable accuracy. Additional constraints on the transition rule are also investigated. The Natural Sciences and Engineering Research Council of Canada (NSERC) and CIENA are acknowledged for financial support.

Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

Ising model of financial markets with many assets

NASA Astrophysics Data System (ADS)

Eckrot, A.; Jurczyk, J.; Morgenstern, I.

2016-11-01

Many models of financial markets exist, but most of them simulate single asset markets. We study a multi asset Ising model of a financial market. Each agent has two possible actions (buy/sell) for every asset. The agents dynamically adjust their coupling coefficients according to past market returns and external news. This leads to fat tails and volatility clustering independent of the number of assets. We find that a separation of news into different channels leads to sector structures in the cross correlations, similar to those found in real markets.

Simulating the Rayleigh-Taylor instability with the Ising model

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

Ball, Justin R.; Elliott, James B.

2011-08-26

The Ising model, implemented with the Metropolis algorithm and Kawasaki dynamics, makes a system with its own physics, distinct from the real world. These physics are sophisticated enough to model behavior similar to the Rayleigh-Taylor instability and by better understanding these physics, we can learn how to modify the system to better re ect reality. For example, we could add a v x and a v y to each spin and modify the exchange rules to incorporate them, possibly using two body scattering laws to construct a more realistic system.

Shearlet-based measures of entropy and complexity for two-dimensional patterns

NASA Astrophysics Data System (ADS)

Brazhe, Alexey

2018-06-01

New spatial entropy and complexity measures for two-dimensional patterns are proposed. The approach is based on the notion of disequilibrium and is built on statistics of directional multiscale coefficients of the fast finite shearlet transform. Shannon entropy and Jensen-Shannon divergence measures are employed. Both local and global spatial complexity and entropy estimates can be obtained, thus allowing for spatial mapping of complexity in inhomogeneous patterns. The algorithm is validated in numerical experiments with a gradually decaying periodic pattern and Ising surfaces near critical state. It is concluded that the proposed algorithm can be instrumental in describing a wide range of two-dimensional imaging data, textures, or surfaces, where an understanding of the level of order or randomness is desired.

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

The Pioneer 11 1976 solar conjunction: A unique opportunity to explore the heliographic latitudinal variations of the solar corona

NASA Technical Reports Server (NTRS)

Berman, A. L.; Wackley, J. A.; Rockwell, S. T.; Yee, J. G.

1976-01-01

The 1976 Pioneer II Solar Conjunction provided the opportunity to accumulate a substantial quantity of doppler noise data over a dynamic range of signal closest approach point heliographic latitudes. The observed doppler noise data were fit to the doppler noise model ISED, and the deviations of the observed doppler noise data from the model were used to construct a (multiplicative) function to describe the effect of heliographic latitude. This expression was then incorporated into the ISED model to produce a new doppler noise model-ISEDB.

Sampling algorithms for validation of supervised learning models for Ising-like systems

NASA Astrophysics Data System (ADS)

Portman, Nataliya; Tamblyn, Isaac

2017-12-01

In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ;ID-MH; that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new ;block-ID; sampling strategy: it decomposes the given structure into square blocks with lattice dimension N ≤ 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).

Self-avoiding walk on a square lattice with correlated vacancies

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Mohammadzadeh, H.; Saber, A.

2018-04-01

The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean-field relation is tested to measure the effect of correlation. After exploring a perturbative Fokker-Planck-like equation, we apply an enriched Rosenbluth Monte Carlo method to study the problem. To be more precise, the winding angle analysis is also performed from which the diffusivity parameter of Schramm-Loewner evolution theory (κ ) is extracted. We find that at the critical Ising (host) system, the exponents are in agreement with Flory's approximation. For the off-critical Ising system, we find also a behavior for the fractal dimension of the walker trace in terms of the correlation length of the Ising system ξ (T ) , i.e., DFSAW(T ) -DFSAW(Tc) ˜1/√{ξ (T ) } .

An electric noise component with density 1/f identified on ISEE 3

NASA Technical Reports Server (NTRS)

Hoang, S.; Steinberg, J. L.; Couturier, P.; Feldman, W. C.

1982-01-01

The properties of the 1/f noise detected at the terminals of ISEE 3 antennas are described and related to the solar wind parameters. The 1/f noise was observed with the radio receivers of the three-dimensional radio mapping experiment using the S and Z dipole antennas. The noise spectra contained a negative spectral index component at frequencies lower than 0.7 of the plasma frequency, and 5-10 times the predicted thermal noise for the Z antenna. S-antenna measurements of the 1/f component revealed it to be deeply spin modulated with a minimum electric field in the direction of the solar wind. Modulation increases with increasing frequency, becomes negligible when the 1/f intensity is negligible with respect to the thermal noise, and increases with solar wind velocity. The possibilities that the noise is due either to waves or currents are discussed.

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.

Accurate Mapping of Multilevel Rydberg Atoms on Interacting Spin-1 /2 Particles for the Quantum Simulation of Ising Models

NASA Astrophysics Data System (ADS)

de Léséleuc, Sylvain; Weber, Sebastian; Lienhard, Vincent; Barredo, Daniel; Büchler, Hans Peter; Lahaye, Thierry; Browaeys, Antoine

2018-03-01

We study a system of atoms that are laser driven to n D3 /2 Rydberg states and assess how accurately they can be mapped onto spin-1 /2 particles for the quantum simulation of anisotropic Ising magnets. Using nonperturbative calculations of the pair potentials between two atoms in the presence of electric and magnetic fields, we emphasize the importance of a careful selection of experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1 /2 Ising models in systems with up to 49 spins, for which numerical simulations become intractable.

Anomalously high potentials observed on ISEE

NASA Technical Reports Server (NTRS)

Whipple, E. C.; Krinsky, I. S.; Torbert, R. B.; Olsen, R. C.

1985-01-01

Data from two electric field experiments and from the plasma composition experiment on ISEE-1 are used to show that the spacecraft charged to close to -70 V in sunlight at 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. The stringent electrostatic cleanliness specifications imposed on ISEE make the presence of differential charging unlikely. Modeling of this event is required to determine if the barrier was produced by the presence of space charge.

Critical phenomena on k -booklets

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-01-01

We define a "k -booklet" to be a set of k semi-infinite planes with -∞

Ising model with conserved magnetization on the human connectome: Implications on the relation structure-function in wakefulness and anesthesia

NASA Astrophysics Data System (ADS)

Stramaglia, S.; Pellicoro, M.; Angelini, L.; Amico, E.; Aerts, H.; Cortés, J. M.; Laureys, S.; Marinazzo, D.

2017-04-01

Dynamical models implemented on the large scale architecture of the human brain may shed light on how a function arises from the underlying structure. This is the case notably for simple abstract models, such as the Ising model. We compare the spin correlations of the Ising model and the empirical functional brain correlations, both at the single link level and at the modular level, and show that their match increases at the modular level in anesthesia, in line with recent results and theories. Moreover, we show that at the peak of the specific heat (the critical state), the spin correlations are minimally shaped by the underlying structural network, explaining how the best match between the structure and function is obtained at the onset of criticality, as previously observed. These findings confirm that brain dynamics under anesthesia shows a departure from criticality and could open the way to novel perspectives when the conserved magnetization is interpreted in terms of a homeostatic principle imposed to neural activity.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

PubMed

Buican, Matthew; Laczko, Zoltan

2018-02-23

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

NASA Astrophysics Data System (ADS)

Buican, Matthew; Laczko, Zoltan

2018-02-01

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Lifted worm algorithm for the Ising model

NASA Astrophysics Data System (ADS)

Elçi, Eren Metin; Grimm, Jens; Ding, Lijie; Nasrawi, Abrahim; Garoni, Timothy M.; Deng, Youjin

2018-04-01

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energylike observable on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energylike observable on the complete graph and leads to a significant constant improvement on toroidal grids.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

PubMed

Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne

2014-08-22

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Universal scaling for the quantum Ising chain with a classical impurity

NASA Astrophysics Data System (ADS)

Apollaro, Tony J. G.; Francica, Gianluca; Giuliano, Domenico; Falcone, Giovanni; Palma, G. Massimo; Plastina, Francesco

2017-10-01

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ ≠1 . In the homogeneous chain limit at μ =1 , we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ =0 , we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ , finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ .

Experimental Mathematics and Mathematical Physics

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

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed Ising system within the effective-field theory and Glauber-type stochastic dynamics approach.

PubMed

Ertaş, Mehmet; Deviren, Bayram; Keskin, Mustafa

2012-11-01

Nonequilibrium magnetic properties in a two-dimensional kinetic mixed spin-2 and spin-5/2 Ising system in the presence of a time-varying (sinusoidal) magnetic field are studied within the effective-field theory (EFT) with correlations. The time evolution of the system is described by using Glauber-type stochastic dynamics. The dynamic EFT equations are derived by employing the Glauber transition rates for two interpenetrating square lattices. We investigate the time dependence of the magnetizations for different interaction parameter values in order to find the phases in the system. We also study the thermal behavior of the dynamic magnetizations, the hysteresis loop area, and dynamic correlation. The dynamic phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane and we observe that the system exhibits dynamic tricritical and reentrant behaviors. Moreover, the system also displays a double critical end point (B), a zero-temperature critical point (Z), a critical end point (E), and a triple point (TP). We also performed a comparison with the mean-field prediction in order to point out the effects of correlations and found that some of the dynamic first-order phase lines, which are artifacts of the mean-field approach, disappeared.

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

Ko, L.F.

Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T < T/sub c/ and T > T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. Inmore » Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations.« less

Evolutionary games with self-questioning adaptive mechanism and the Ising model

NASA Astrophysics Data System (ADS)

Liu, J.; Xu, C.; Hui, P. M.

2017-09-01

A class of evolutionary games using a self-questioning strategy switching mechanism played in a population of connected agents is shown to behave as an Ising model Hamiltonian of spins connected in the same way. The payoff parameters combine to give the coupling between spins and an external magnetic field. The mapping covers the prisoner's dilemma, snowdrift and stag hunt games in structured populations. A well-mixed system is used to illustrate the equivalence. In a chain of agents/spins, the mapping to Ising model leads to an exact solution to the games effortlessly. The accuracy of standard approximations on the games can then be quantified. The site approximation is found to show varied accuracies depending on the payoff parameters, and the link approximation is shown to give the exact result in a chain but not in a closed form. The mapping established here connects two research areas, with each having much to offer to the other.

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.

Potentiometric detection of chemical vapors using molecularly imprinted polymers as receptors

PubMed Central

Liang, Rongning; Chen, Lusi; Qin, Wei

2015-01-01

Ion-selective electrode (ISE) based potentiometric gas sensors have shown to be promising analytical tools for detection of chemical vapors. However, such sensors are only capable of detecting those vapors which can be converted into ionic species in solution. This paper describes for the first time a polymer membrane ISE based potentiometric sensing system for sensitive and selective determination of neutral vapors in the gas phase. A molecularly imprinted polymer (MIP) is incorporated into the ISE membrane and used as the receptor for selective adsorption of the analyte vapor from the gas phase into the sensing membrane phase. An indicator ion with a structure similar to that of the vapor molecule is employed to indicate the change in the MIP binding sites in the membrane induced by the molecular recognition of the vapor. The toluene vapor is used as a model and benzoic acid is chosen as its indicator. Coupled to an apparatus manifold for preparation of vapor samples, the proposed ISE can be utilized to determine volatile toluene in the gas phase and allows potentiometric detection down to parts per million levels. This work demonstrates the possibility of developing a general sensing principle for detection of neutral vapors using ISEs. PMID:26215887

Direct imaging of coexisting ordered and frustrated sublattices in artificial ferromagnetic quasicrystals

DOE PAGES

Farmer, B.; Bhat, V. S.; Balk, A.; ...

2016-04-25

Here, we have used scanning electron microscopy with polarization analysis and photoemission electron microscopy to image the two-dimensional magnetization of permalloy films patterned into Penrose P2 tilings (P2T). The interplay of exchange interactions in asymmetrically coordinated vertices and short-range dipole interactions among connected film segments stabilize magnetically ordered, spatially distinct sublattices that coexist with frustrated sublattices at room temperature. Numerical simulations that include long-range dipole interactions between sublattices agree with images of as-grown P2T samples and predict a magnetically ordered ground state for a two-dimensional quasicrystal lattice of classical Ising spins.

From near to eternity: Spin-glass planting, tiling puzzles, and constraint-satisfaction problems

NASA Astrophysics Data System (ADS)

Hamze, Firas; Jacob, Darryl C.; Ochoa, Andrew J.; Perera, Dilina; Wang, Wenlong; Katzgraber, Helmut G.

2018-04-01

We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model defined on a cubic lattice, where subproblems, whose couplers are restricted to the two values {-1 ,+1 } , are specified on unit cubes and are parametrized by their local degeneracy. The construction is shown to be equivalent to a type of three-dimensional constraint-satisfaction problem known as the tiling puzzle. By varying the proportions of subproblem types, the Hamiltonian can span a dramatic range of typical computational complexity, from fairly easy to many orders of magnitude more difficult than prototypical bimodal and Gaussian spin glasses in three space dimensions. We corroborate this behavior via experiments with different algorithms and discuss generalizations and extensions to different types of graphs.

Implicit and Explicit Self-Esteem in Current, Remitted, Recovered, and Comorbid Depression and Anxiety Disorders: The NESDA Study

PubMed Central

van Tuijl, Lonneke A.; Glashouwer, Klaske A.; Bockting, Claudi L. H.; Tendeiro, Jorge N.; Penninx, Brenda W. J. H.; de Jong, Peter J.

2016-01-01

Background Dual processing models of psychopathology emphasize the relevance of differentiating between deliberative self-evaluative processes (explicit self-esteem; ESE) and automatically-elicited affective self-associations (implicit self-esteem; ISE). It has been proposed that both low ESE and ISE would be involved in major depressive disorder (MDD) and anxiety disorders (AD). Further, it has been hypothesized that MDD and AD may result in a low ISE “scar” that may contribute to recurrence after remission. However, the available evidence provides no straightforward support for the relevance of low ISE in MDD/AD, and studies testing the relevance of discrepant SE even showed that especially high ISE combined with low ESE is predictive of the development of internalizing symptoms. However, these earlier findings have been limited by small sample sizes, poorly defined groups in terms of comorbidity and phase of the disorders, and by using inadequate indices of discrepant SE. Therefore, this study tested further the proposed role of ISE and discrepant SE in a large-scale study allowing for stricter differentiation between groups and phase of disorder. Method In the context of the Netherlands Study of Depression and Anxiety (NESDA), we selected participants with current MDD (n = 60), AD (n = 111), and comorbid MDD/AD (n = 71), remitted MDD (n = 41), AD (n = 29), and comorbid MDD/AD (n = 14), recovered MDD (n = 136) and AD (n = 98), and never MDD or AD controls (n = 382). The Implicit Association Test was used to index ISE and the Rosenberg Self-Esteem Scale indexed ESE. Results Controls reported higher ESE than all other groups, and current comorbid MDD/AD had lower ESE than all other clinical groups. ISE was only lower than controls in current comorbid AD/MDD. Discrepant self-esteem (difference between ISE and ESE) was not associated with disorder status once controlling for ESE. Limitations Cross-sectional design limits causal inferences. Conclusion Findings suggest a prominent role for ESE in MDD and AD, while in comorbid MDD/AD negative self-evaluations are also present at the implicit level. There was no evidence to support the view that AD and MDD would result in a low ISE “scar”. PMID:27846292

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

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

Murtazaev, A. K.; Ramazanov, M. K., E-mail: sheikh77@mail.ru; Kassan-Ogly, F. A.

2015-01-15

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.

Critical frontier of the triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Qian, Xiaofeng; Wegewijs, Maarten; Blöte, Henk W.

2004-03-01

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.

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

Basu, Banasri; Bandyopadhyay, Pratul; Majumdar, Priyadarshi

We have studied quantum phase transition induced by a quench in different one-dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one-dimensional spin chains. At themore » critical region, the entanglement entropy of a block of L spins with the rest of the system is also estimated which is found to increase logarithmically with L. The dependence on the quench time puts a constraint on the block size L. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the XXX model and Ising model with magnetic field in the negative z axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.« less

Parameter diagnostics of phases and phase transition learning by neural networks

NASA Astrophysics Data System (ADS)

Suchsland, Philippe; Wessel, Stefan

2018-05-01

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.

Ising order in a magnetized Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Chan, Yang-Hao; Jin, Wen; Jiang, Hong-Chen; Starykh, Oleg A.

2017-12-01

We report a combined analytical and density matrix renormalized group study of the antiferromagnetic X X Z spin-1 /2 Heisenberg chain subject to a uniform Dzyaloshinskii-Moriya (DM) interaction and a transverse magnetic field. The numerically determined phase diagram of this model, which features two ordered Ising phases and a critical Luttinger liquid, one with fully broken spin-rotational symmetry, agrees well with the predictions of Garate and Affleck [I. Garate and I. Affleck, Phys. Rev. B 81, 144419 (2010), 10.1103/PhysRevB.81.144419]. We also confirm the prevalence of the Nz Néel Ising order in the regime of comparable DM and magnetic field magnitudes.

One Dimensional(1D)-to-2D Crossover of Spin Correlations in the 3D Magnet ZnMn 2O 4

DOE PAGES

Disseler, S. M.; Chen, Y.; Yeo, S.; ...

2015-12-08

In this paper we report on the intriguing evolution of the dynamical spin correlations of the frustrated spinel ZnMn 2O 4. Inelastic neutron scattering and magnetization studies reveal that the dynamical correlations at high temperatures are 1D. At lower temperature, these dynamical correlations become 2D. Surprisingly, the dynamical correlations condense into a quasi 2D Ising-like ordered state, making this a rare observation of two dimensional order on the spinel lattice. Remarkably, 3D ordering is not observed down to temperatures as low as 300 mK. This unprecedented dimensional crossover stems from frustrated exchange couplings due to the huge Jahn-Teller distortions aroundmore » Mn 3+ ions on the spinel lattice.« less

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

NASA Technical Reports Server (NTRS)

Bentz, Daniel N.; Betush, William; Jackson, Kenneth A.

2003-01-01

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Effect of increasing disorder on domains of the 2d Coulomb glass.

PubMed

Bhandari, Preeti; Malik, Vikas

2017-12-06

We have studied a two dimensional lattice model of Coulomb glass for a wide range of disorders at [Formula: see text]. The system was first annealed using Monte Carlo simulation. Further minimization of the total energy of the system was done using an algorithm developed by Baranovskii et al, followed by cluster flipping to obtain the pseudo-ground states. We have shown that the energy required to create a domain of linear size L in d dimensions is proportional to [Formula: see text]. Using Imry-Ma arguments given for random field Ising model, one gets critical dimension [Formula: see text] for Coulomb glass. The investigation of domains in the transition region shows a discontinuity in staggered magnetization which is an indication of a first-order type transition from charge-ordered phase to disordered phase. The structure and nature of random field fluctuations of the second largest domain in Coulomb glass are inconsistent with the assumptions of Imry and Ma, as was also reported for random field Ising model. The study of domains showed that in the transition region there were mostly two large domains, and that as disorder was increased the two large domains remained, but a large number of small domains also opened up. We have also studied the properties of the second largest domain as a function of disorder. We furthermore analysed the effect of disorder on the density of states, and showed a transition from hard gap at low disorders to a soft gap at higher disorders. At [Formula: see text], we have analysed the soft gap in detail, and found that the density of states deviates slightly ([Formula: see text]) from the linear behaviour in two dimensions. Analysis of local minima show that the pseudo-ground states have similar structure.

Renormalization of concurrence: The application of the quantum renormalization group to quantum-information systems

NASA Astrophysics Data System (ADS)

Kargarian, M.; Jafari, R.; Langari, A.

2007-12-01

We have combined the idea of renormalization group and quantum-information theory. We have shown how the entanglement or concurrence evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. Moreover, we introduce how the renormalization-group approach can be implemented to obtain the quantum-information properties of a many-body system. We have obtained the concurrence as a measure of entanglement, its derivatives and their scaling behavior versus the size of system for the one-dimensional Ising model in transverse field. We have found that the derivative of concurrence between two blocks each containing half of the system size diverges at the critical point with the exponent, which is directly associated with the divergence of the correlation length.

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

Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel

We study 1+1 dimensional Φ 4 theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C≤C max, we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along themore » full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model.« less

Analysis and optimization of population annealing

NASA Astrophysics Data System (ADS)

Amey, Christopher; Machta, Jonathan

2018-03-01

Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well suited for simulating the equilibrium properties of systems with rough free-energy landscapes. In this work we seek to understand and improve the performance of population annealing. We derive several useful relations between quantities that describe the performance of population annealing and use these relations to suggest methods to optimize the algorithm. These optimization methods were tested by performing large-scale simulations of the three-dimensional (3D) Edwards-Anderson (Ising) spin glass and measuring several observables. The optimization methods were found to substantially decrease the amount of computational work necessary as compared to previously used, unoptimized versions of population annealing. We also obtain more accurate values of several important observables for the 3D Edwards-Anderson model.

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.

Error threshold for color codes and random three-body Ising models.

PubMed

Katzgraber, Helmut G; Bombin, H; Martin-Delgado, M A

2009-08-28

We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation, and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random three-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p(c) = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities do not necessarily imply lower resistance to noise.

Monte Carlo technique for very large ising models

NASA Astrophysics Data System (ADS)

Kalle, C.; Winkelmann, V.

1982-08-01

Rebbi's multispin coding technique is improved and applied to the kinetic Ising model with size 600*600*600. We give the central part of our computer program (for a CDC Cyber 76), which will be helpful also in a simulation of smaller systems, and describe the other tricks necessary to go to large lattices. The magnetization M at T=1.4* T c is found to decay asymptotically as exp(-t/2.90) if t is measured in Monte Carlo steps per spin, and M( t = 0) = 1 initially.

Modelling Polar Self Assembly

NASA Astrophysics Data System (ADS)

Olvera de La Cruz, Monica; Sayar, Mehmet; Solis, Francisco J.; Stupp, Samuel I.

2001-03-01

Recent experimental studies in our group have shown that self assembled thin films of noncentrosymmetric supramolecular objects composed of triblock rodcoil molecules exhibit finite polar order. These aggregates have both long range dipolar and short range Ising-like interactions. We study the ground state of a simple model with these competing interactions. We find that the competition between Ising-like and dipolar forces yield a periodic domain structure, which can be controlled by adjusting the force constants and film thickness. When the surface forces are included in the potential, the system exhibits a finite macroscopic polar order.

Interacting damage models mapped onto ising and percolation models

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

Toussaint, Renaud; Pride, Steven R.

The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in themore » system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard statistical mechanics.« less

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Environment overwhelms both nature and nurture in a model spin glass

NASA Astrophysics Data System (ADS)

Middleton, A. Alan; Yang, Jie

We are interested in exploring what information determines the particular history of the glassy long term dynamics in a disordered material. We study the effect of initial configurations and the realization of stochastic dynamics on the long time evolution of configurations in a two-dimensional Ising spin glass model. The evolution of nearest neighbor correlations is computed using patchwork dynamics, a coarse-grained numerical heuristic for temporal evolution. The dependence of the nearest neighbor spin correlations at long time on both initial spin configurations and noise histories are studied through cross-correlations of long-time configurations and the spin correlations are found to be independent of both. We investigate how effectively rigid bond clusters coarsen. Scaling laws are used to study the convergence of configurations and the distribution of sizes of nearly rigid clusters. The implications of the computational results on simulations and phenomenological models of spin glasses are discussed. We acknowledge NSF support under DMR-1410937 (CMMT program).

Two-dimensional lattice gauge theories with superconducting quantum circuits

PubMed Central

Marcos, D.; Widmer, P.; Rico, E.; Hafezi, M.; Rabl, P.; Wiese, U.-J.; Zoller, P.

2014-01-01

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability. PMID:25512676

AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems.

PubMed

LeVine, Michael V; Weinstein, Harel

2015-05-01

In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular "action at a distance" is termed allostery . Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.

Absence of long-range order in the frustrated magnet SrDy2O4 due to trapped defects from a dimensionality crossover

NASA Astrophysics Data System (ADS)

Gauthier, N.; Fennell, A.; Prévost, B.; Uldry, A.-C.; Delley, B.; Sibille, R.; Désilets-Benoit, A.; Dabkowska, H. A.; Nilsen, G. J.; Regnault, L.-P.; White, J. S.; Niedermayer, C.; Pomjakushin, V.; Bianchi, A. D.; Kenzelmann, M.

2017-04-01

Magnetic frustration and low dimensionality can prevent long-range magnetic order and lead to exotic correlated ground states. SrDy2O4 consists of magnetic Dy3 + ions forming magnetically frustrated zigzag chains along the c axis and shows no long-range order to temperatures as low as T =60 mK. We carried out neutron scattering and ac magnetic susceptibility measurements using powder and single crystals of SrDy2O4 . Diffuse neutron scattering indicates strong one-dimensional (1D) magnetic correlations along the chain direction that can be qualitatively accounted for by the axial next-nearest-neighbor Ising model with nearest-neighbor and next-nearest-neighbor exchange J1=0.3 meV and J2=0.2 meV, respectively. Three-dimensional (3D) correlations become important below T*≈0.7 K. At T =60 mK, the short-range correlations are characterized by a putative propagation vector k1 /2=(0 ,1/2 ,1/2 ) . We argue that the absence of long-range order arises from the presence of slowly decaying 1D domain walls that are trapped due to 3D correlations. This stabilizes a low-temperature phase without long-range magnetic order, but with well-ordered chain segments separated by slowly moving domain walls.

Parallel tempering simulation of the three-dimensional Edwards-Anderson model with compact asynchronous multispin coding on GPU

NASA Astrophysics Data System (ADS)

Fang, Ye; Feng, Sheng; Tam, Ka-Ming; Yun, Zhifeng; Moreno, Juana; Ramanujam, J.; Jarrell, Mark

2014-10-01

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional 28.4% speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 ps per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.

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2011-01-31

...); ISE Semiconductors (BYT); ISE Electronic Trading (DMA); ISE-Revere Natural Gas (FUM); ISE Water (HHO... SECURITIES AND EXCHANGE COMMISSION [Release No. 34-63761; File No. SR-ISE-2011-04] Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing of Proposed Rule Change To Establish a...

Transverse fields to tune an Ising-nematic quantum phase transition [Transverse fields to tune an Ising-nematic quantum critical transition

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

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.

Here, the paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated withmore » spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.« less

Transverse fields to tune an Ising-nematic quantum phase transition [Transverse fields to tune an Ising-nematic quantum critical transition

DOE PAGES

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.; ...

2017-12-05

Here, the paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated withmore » spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.« less

2D Spin Crossover Nanoparticles described by the Ising-like model solved in Local Mean-Field Approximation

NASA Astrophysics Data System (ADS)

Eddine Allal, Salah; Linares, Jorge; Boukheddaden, K.; Dahoo, Pierre Richard; de Zela, F.

2017-12-01

Some six-coordinate iron (II) coordination compounds exhibit thermal-, optical-, electrical-, magnetic- and pressure-induced switching between the diamagnetic low-spin (LS, S=0) and the paramagnetic high-spin (HS; S=2) states [1]. This may lead to potential application of these complexes in molecular devices such as temperature and pressure sensors [2]. An Ising-like model has been proposed to explain the occurrence of the thermal hysteresis behaviour [3,4] of this switchable solids. In this contribution, the local mean field approximation is applied to solve the Hamiltonian modelling interactions pertaining to 2D nanoparticles embedded in a magnetically-inactive matrix.

A model of the near-earth plasma environment and application to the ISEE-A and -B orbit

NASA Technical Reports Server (NTRS)

Chan, K. W.; Sawyer, K. W.; Vette, J. I.

1977-01-01

A model of the near-earth environment to obtain a best estimate of the average flux of protons and electrons in the energy range from 0.1 to 100 keV for the International Sun-Earth Explorer (ISEE)-A and -B spacecraft. The possible radiation damage to the thermal coating on these spinning spacecraft is also studied. Applications of the model to other high-altitude satellites can be obtained with the appropriate orbit averaging. This study is the first attempt to synthesize an overall quantitative environment of low-energy particles for high altitude spacecraft, using data from in situ measurements.

Correction of defective pixels for medical and space imagers based on Ising Theory

NASA Astrophysics Data System (ADS)

Cohen, Eliahu; Shnitser, Moriel; Avraham, Tsvika; Hadar, Ofer

2014-09-01

We propose novel models for image restoration based on statistical physics. We investigate the affinity between these fields and describe a framework from which interesting denoising algorithms can be derived: Ising-like models and simulated annealing techniques. When combined with known predictors such as Median and LOCO-I, these models become even more effective. In order to further examine the proposed models we apply them to two important problems: (i) Digital Cameras in space damaged from cosmic radiation. (ii) Ultrasonic medical devices damaged from speckle noise. The results, as well as benchmark and comparisons, suggest in most of the cases a significant gain in PSNR and SSIM in comparison to other filters.

OpenCL Implementation of NeuroIsing

NASA Astrophysics Data System (ADS)

Zapart, C. A.

Recent advances in graphics card hardware combined with anintroduction of the OpenCL standard promise to accelerate numerical simulations across diverse scientific disciplines. One such field benefiting from new hardware/software paradigms is econophysics. The paper describes an OpenCL implementation of a selected econophysics model: NeuroIsing, which has been designed to execute in parallel on a vendor-independent graphics card. Originally introduced in the paper [C.~A.~Zapart, ``Econophysics in Financial Time Series Prediction'', PhD thesis, Graduate University for Advanced Studies, Japan (2009)], at first it was implemented on a CELL processor running inside a SONY PS3 games console. The NeuroIsing framework can be applied to predicting and trading foreign exchange as well as stock market index futures.

ISE structural dynamic experiments

NASA Technical Reports Server (NTRS)

Lock, Malcolm H.; Clark, S. Y.

1988-01-01

The topics are presented in viewgraph form and include the following: directed energy systems - vibration issue; Neutral Particle Beam Integrated Space Experiment (NPB-ISE) opportunity/study objective; vibration sources/study plan; NPB-ISE spacecraft configuration; baseline slew analysis and results; modal contributions; fundamental pitch mode; vibration reduction approaches; peak residual vibration; NPB-ISE spacecraft slew experiment; goodbye ISE - hello Zenith Star Program.

Average configuration of the distant (less than 220-earth-radii) magnetotail - Initial ISEE-3 magnetic field results

NASA Technical Reports Server (NTRS)

Slavin, J. A.; Tsurutani, B. T.; Smith, E. J.; Jones, D. E.; Sibeck, D. G.

1983-01-01

Magnetic field measurements from the first two passes of the ISEE-3 GEOTAIL Mission have been used to study the structure of the trans-lunar tail. Good agreement was found between the ISEE-3 magnetopause crossings and the Explorer 33, 35 model of Howe and Binsack (1972). Neutral sheet location was well ordered by the hinged current sheet models based upon near earth measurements. Between X = -20 and -120 earth radii the radius of the tail increases by about 30 percent while the lobe field strength decreases by approximately 60 percent. Beyond X = -100 to -1200 earth radii the tail diameter and lobe field magnitude become nearly constant at terminal values of approximately 60 earth radii and 9 nT, respectively. The distance at which the tail was observed to cease flaring, 100-120 earth radii, is in close agreement with the predictions of the analytic tail model of Coroniti and Kennel (1972). Overall, the findings of this study suggest that the magnetotail retains much of its near earth structure out to X = -220 earth radii.

Exact sampling hardness of Ising spin models

NASA Astrophysics Data System (ADS)

Fefferman, B.; Foss-Feig, M.; Gorshkov, A. V.

2017-09-01

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

Frustrated spin-1/2 Ising antiferromagnet on a square lattice in a transverse field

NASA Astrophysics Data System (ADS)

Bobák, A.; Jurčišinová, E.; Jurčišin, M.; Žukovič, M.

2018-02-01

We investigate the phase transitions and tricritical behaviors of the frustrated Ising antiferromagnet with first- (J1<0 ) and second- (J2<0 ) nearest-neighbor interactions in a transverse field Ω on the square lattice using an effective-field theory with correlations based on a single-spin approximation. We have proposed a functional for the free energy to obtain the phase diagram in the T -R (R =J2/|J1| ) or T -Ω planes. It is shown that due to the transverse field the phase transition between ordered and disordered phases changes in the tricritical point (TCP) from the second order to the first order. The longitudinal and transverse magnetizations are also studied for selected values of R and Ω . In particular, the variation of TCP at the ground state in the three-dimensional space is constructed. For some special cases, values of the critical temperature and the critical transverse field have been determined analytically.

Correspondence between spanning trees and the Ising model on a square lattice

NASA Astrophysics Data System (ADS)

Viswanathan, G. M.

2017-06-01

An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function T (z ) gives the spanning tree constant when evaluated at z =1 , while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function Z (K ) of the Ising model evaluated at the critical temperature K =Kc is related to T (1 ) . Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K ) s e c h 2 K ] 2=k exp[T (k )] , where k =2 tanh(2 K )s e c h (2 K ) . The identical Mahler measure connects the two seemingly disparate quantities T (z ) and Z (K ) . In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.

77 FR 21615 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and...

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2012-04-10

... by ISE. The first note relates to Non-ISE Market Maker fees, which apply to regular and complex orders, and how those fees are applied to execution of complex orders on the Exchange.\\3\\ Non-ISE Market Maker fees were adopted by ISE in 2006.\\4\\ Prior to this fee change, Non-ISE Market Makers were subject...

Identification of ground-state spin ordering in antiferromagnetic transition metal oxides using the Ising model and a genetic algorithm

PubMed Central

Lee, Kyuhyun; Youn, Yong; Han, Seungwu

2017-01-01

Abstract We identify ground-state collinear spin ordering in various antiferromagnetic transition metal oxides by constructing the Ising model from first-principles results and applying a genetic algorithm to find its minimum energy state. The present method can correctly reproduce the ground state of well-known antiferromagnetic oxides such as NiO, Fe2O3, Cr2O3 and MnO2. Furthermore, we identify the ground-state spin ordering in more complicated materials such as Mn3O4 and CoCr2O4. PMID:28458746

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.

Renormalization group, normal form theory and the Ising model

NASA Astrophysics Data System (ADS)

Raju, Archishman; Hayden, Lorien; Clement, Colin; Liarte, Danilo; Sethna, James

The results of the renormalization group are commonly advertised as the existence of power law singularities at critical points. Logarithmic and exponential corrections are seen as special cases and dealt with on a case-by-case basis. We propose to systematize computing the singularities in the renormalization group using perturbative normal form theory. This gives us a way to classify all such singularities in a unified framework and to generate a systematic machinery to do scaling collapses. We show that this procedure leads to some new results even in classic cases like the Ising model and has general applicability.

Magnetic phase diagram, static properties and relaxation of the insulating spin glass Co 1- xMn x(SCN) 2(CH 3OH) 2

NASA Astrophysics Data System (ADS)

DeFotis, G. C.; Just, E. M.; Pugh, V. J.; Coffey, G. A.; Hogg, B. D.; Fitzhenry, S. L.; Marmorino, J. L.; Krovich, D. J.; Chamberlain, R. V.

1999-07-01

The magnetic behavior of Co 1- xMn x(SCN) 2(CH 3OH) 2 has been studied by DC magnetization and susceptibility measurements on mixtures spanning the complete composition range. The pure components are a quasi-two-dimensional Heisenberg antiferromagnet (Mn system) and a three-dimensional Ising antiferromagnet (Co system). The crystal structure of the cobalt constituent is determined, and is closely related to that of the manganese constituent. Competing orthogonal spin anisotropies should occur in mixtures, and frustration effects arising from competing ferromagnetic and antiferromagnetic interactions may also arise. The Curie and Weiss constants, in χM= C/( T- θ), vary regularly with composition. C versus x is essentially linear while θ versus x shows a definite curvature, analysis of which reveals that the unlike-ion exchange interaction is antiferromagnetic and stronger than the like-ion interactions. The magnetic susceptibility is field dependent, more markedly so with increasing x. Plots of M/ H versus T exhibit maxima at low temperatures only for mixtures substantially richer in cobalt than manganese. Magnetic transition temperatures are estimated from these data. Magnetization versus field isotherms evolve with composition and with temperature; those for x=0.24 5 and 0.16 9 exhibit S-shapes for temperatures at or below the identified transitions. The nonlinear susceptibility versus temperature for x=0.24 5 displays structure but does not diverge. The temperature dependence of the thermoremanent magnetization (TRM) for x=0.24 5 shows characteristic features but does not follow any simple form. The time-dependence of the TRM is fitted at a series of temperatures employing a stretched exponential decay form. The thermal variation of the fit parameters is systematic and suggests that temperatures just below 3 K and slightly above 6 K have special significance. Over a limited temperature range the TRM is found to scale approximately as T log10(t/τ 0) , with τ0≈10 -12 s. Strong and weak irreversibility lines are determined for x=0.24 5; both vary as τg∝ h0.56, with zero-field temperatures of Ts(0)=5.5 5 K and Tw(0)=9.8 5 K, respectively. The exponent is closer to that recently predicted (0.53) for a short-range three-dimensional Ising spin glass than to the value 2/3 of the DeAlmeida-Thouless line in the infinite range mean-field Ising model. The existence of strong random anisotropy may account for the presence of a weak irreversibility line with the observed exponent. The T- x magnetic phase diagram exhibits a crossing of paramagnetic-ordered state phase boundaries and an associated tetracritical point at x≈0.20 5 and T≈2.6 0 K. Spin glass properties are apparent for compositions close to the tetracritical point.

Hearing the shape of the Ising model with a programmable superconducting-flux annealer.

PubMed

Vinci, Walter; Markström, Klas; Boixo, Sergio; Roy, Aidan; Spedalieri, Federico M; Warburton, Paul A; Severini, Simone

2014-07-16

Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.

Dynamics of the Random Field Ising Model

NASA Astrophysics Data System (ADS)

Xu, Jian

The Random Field Ising Model (RFIM) is a general tool to study disordered systems. Crackling noise is generated when disordered systems are driven by external forces, spanning a broad range of sizes. Systems with different microscopic structures such as disordered mag- nets and Earth's crust have been studied under the RFIM. In this thesis, we investigated the domain dynamics and critical behavior in two dipole-coupled Ising ferromagnets Nd2Fe14B and LiHoxY 1-xF4. With Tc well above room temperature, Nd2Fe14B has shown reversible disorder when exposed to an external transverse field and crosses between two universality classes in the strong and weak disorder limits. Besides tunable disorder, LiHoxY1-xF4 has shown quantum tunneling effects arising from quantum fluctuations, providing another mechanism for domain reversal. Universality within and beyond power law dependence on avalanche size and energy were studied in LiHo0.65Y0.35 F4.

Ising-like patterns of spatial synchrony in population biology

NASA Astrophysics Data System (ADS)

Noble, Andrew; Hastings, Alan; Machta, Jon

2014-03-01

Systems of coupled dynamical oscillators can undergo a phase transition between synchronous and asynchronous phases. In the case of coupled map lattices, the spontaneous symmetry breaking of a temporal-phase order parameter is known to exhibit Ising-like critical behavior. Here, we investigate a noisy coupled map motivated by the study of spatial synchrony in ecological populations far from the extinction threshold. Ising-like patterns of criticality, as well as spinodal decomposition and homogeneous nucleation, emerge from the nonlinear interactions of environmental fluctuations in habitat quality, local density-dependence in reproduction, and dispersal. In the mean-field limit, the correspondence to the Ising model is exact: the fixed points of our dynamical system are given by the equation of state for Weiss mean-field theory under an appropriate mapping of parameters. We have strong evidence that a quantitative correspondence persists, both near and far from the critical point, in the presence of fluctuations. Our results provide a formal connection between equilibrium statistical physics and population biology. This work is supported by the National Science Foundation under Grant No. 1344187.

Analysing and controlling the tax evasion dynamics via majority-vote model

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2010-09-01

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdös-Rényi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical qc to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies cited above giving the same behavior regardless of dynamic or topology used here.

Ginzburg criterion for ionic fluids: the effect of Coulomb interactions.

PubMed

Patsahan, O

2013-08-01

The effect of the Coulomb interactions on the crossover between mean-field and Ising critical behavior in ionic fluids is studied using the Ginzburg criterion. We consider the charge-asymmetric primitive model supplemented by short-range attractive interactions in the vicinity of the gas-liquid critical point. The model without Coulomb interactions exhibiting typical Ising critical behavior is used to calibrate the Ginzburg temperature of the systems comprising electrostatic interactions. Using the collective variables method, we derive a microscopic-based effective Hamiltonian for the full model. We obtain explicit expressions for all the relevant Hamiltonian coefficients within the framework of the same approximation, i.e., the one-loop approximation. Then we consistently calculate the reduced Ginzburg temperature t(G) for both the purely Coulombic model (a restricted primitive model) and the purely nonionic model (a hard-sphere square-well model) as well as for the model parameters ranging between these two limiting cases. Contrary to the previous theoretical estimates, we obtain the reduced Ginzburg temperature for the purely Coulombic model to be about 20 times smaller than for the nonionic model. For the full model including both short-range and long-range interactions, we show that t(G) approaches the value found for the purely Coulombic model when the strength of the Coulomb interactions becomes sufficiently large. Our results suggest a key role of Coulomb interactions in the crossover behavior observed experimentally in ionic fluids as well as confirm the Ising-like criticality in the Coulomb-dominated ionic systems.

Visualization tool for three-dimensional plasma velocity distributions (ISEE_3D) as a plug-in for SPEDAS

NASA Astrophysics Data System (ADS)

Keika, Kunihiro; Miyoshi, Yoshizumi; Machida, Shinobu; Ieda, Akimasa; Seki, Kanako; Hori, Tomoaki; Miyashita, Yukinaga; Shoji, Masafumi; Shinohara, Iku; Angelopoulos, Vassilis; Lewis, Jim W.; Flores, Aaron

2017-12-01

This paper introduces ISEE_3D, an interactive visualization tool for three-dimensional plasma velocity distribution functions, developed by the Institute for Space-Earth Environmental Research, Nagoya University, Japan. The tool provides a variety of methods to visualize the distribution function of space plasma: scatter, volume, and isosurface modes. The tool also has a wide range of functions, such as displaying magnetic field vectors and two-dimensional slices of distributions to facilitate extensive analysis. The coordinate transformation to the magnetic field coordinates is also implemented in the tool. The source codes of the tool are written as scripts of a widely used data analysis software language, Interactive Data Language, which has been widespread in the field of space physics and solar physics. The current version of the tool can be used for data files of the plasma distribution function from the Geotail satellite mission, which are publicly accessible through the Data Archives and Transmission System of the Institute of Space and Astronautical Science (ISAS)/Japan Aerospace Exploration Agency (JAXA). The tool is also available in the Space Physics Environment Data Analysis Software to visualize plasma data from the Magnetospheric Multiscale and the Time History of Events and Macroscale Interactions during Substorms missions. The tool is planned to be applied to data from other missions, such as Arase (ERG) and Van Allen Probes after replacing or adding data loading plug-ins. This visualization tool helps scientists understand the dynamics of space plasma better, particularly in the regions where the magnetohydrodynamic approximation is not valid, for example, the Earth's inner magnetosphere, magnetopause, bow shock, and plasma sheet.

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Ultrathin nanosheets of CrSiTe 3. A semiconducting two-dimensional ferromagnetic material

DOE PAGES

Lin, Ming -Wei; Zhung, Houlong L.; Yan, Jiaqiang; ...

2015-11-27

Finite range ferromagnetism and antiferromagnetism in two-dimensional (2D) systems within an isotropic Heisenberg model at non-zero temperature were originally proposed to be impossible. However, recent theoretical studies using an Ising model have recently shown that 2D magnetic crystals can exhibit magnetism. Experimental verification of existing 2D magnetic crystals in this system has remained elusive. In this work we for the first time exfoliate the CrSiTe 3, a bulk ferromagnetic semiconductor, to mono- and few-layer 2D crystals onto a Si/SiO 2 substrate. The Raman spectra show the good stability and high quality of the exfoliated flakes, consistent with the computed phononmore » spectra of 2D CrSiTe 3, giving a strong evidence for the existence of 2D CrSiTe 3 crystals. When the thickness of the CrSiTe 3 crystals is reduced to few-layers, we observed a clear change in resistivity at 80~120 K, consistent with the theoretical calculations on the Curie temperature (Tc) of ~80 K for the magnetic ordering of 2D CrSiTe 3 crystals. As a result, the ferromagnetic mono- and few-layer 2D CrSiTe 3 indicated here should enable numerous applications in nano-spintronics.« less

Diffusion on an Ising chain with kinks

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Mansour, Toufik; Severini, Simone

2009-07-01

We count the number of histories between the two degenerate minimum energy configurations of the Ising model on a chain, as a function of the length n and the number d of kinks that appear above the critical temperature. This is equivalent to count permutations of length n avoiding certain subsequences depending on d. We give explicit generating functions and compute the asymptotics. The setting considered has a role when describing dynamics induced by quantum Hamiltonians with deconfined quasi-particles.

Stochastic thermodynamics for Ising chain and symmetric exclusion process.

PubMed

Toral, R; Van den Broeck, C; Escaff, D; Lindenberg, Katja

2017-03-01

We verify the finite-time fluctuation theorem for a linear Ising chain in contact with heat reservoirs at its ends. Analytic results are derived for a chain consisting of two spins. The system can be mapped onto a model for particle transport, namely, the symmetric exclusion process in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.

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.

Unusual specific heat of almost dry L-cysteine and L-cystine amino acids.

PubMed

Ishikawa, M S; Lima, T A; Ferreira, F F; Martinho, H S

2015-03-01

A detailed quantitative analysis of the specific heat in the 0.5- to 200-K temperature range for almost dry L-cysteine and its dimer, L-cystine, amino acids is presented. We report the occurrence of a sharp first-order transition at ∼76 K for L-cysteine associated with the thiol group ordering which was successfully modeled with the two-dimensional Ising model. We demonstrated that quantum rotors, two-level systems (TLS), Einstein oscillators, and acoustic phonons (the Debye model) are essential ingredients to correctly describe the overall experimental data. Our analysis pointed out the absence of the TLS contribution to the low temperature specific heat of L-cysteine. This result was similar to that found in other noncrystalline amorphous materials, e.g., amorphous silicon, low density amorphous water, and ultrastable glasses. L-cystine presented an unusual nonlinear acoustic dispersion relation ω(q)=vq0.95 and a Maxwell-Boltzmann-type distribution of tunneling barriers. The presence of Einstein oscillators with ΘE∼70 K was common in both systems and adequately modeled the boson peak contributions.

Interface tension in the improved Blume-Capel model

NASA Astrophysics Data System (ADS)

Hasenbusch, Martin

2017-09-01

We study interfaces with periodic boundary conditions in the low-temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with antiperiodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension σ and the correlation length ξ obtained in previous work, we determine the universal amplitude ratios R2 nd ,+=σ0f2nd ,+ 2=0.3863 (6 ) , R2 nd ,-=σ0f2nd ,- 2=0.1028 (1 ) , and Rexp ,-=σ0fexp,- 2=0.1077 (3 ) . Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.

CAISE: A NSF Resource Center for Informal Science Education

NASA Astrophysics Data System (ADS)

Dickow, Benjamin

2012-01-01

Informal science education (ISE) is playing an increasingly important role in how and where the public engages with science. A growing body of research is showing that people learn the majority of their science knowledge outside of school (Falk & Dierking, 2010). The ISE field includes a wide variety of sources, including the internet, TV programs, magazines, hobby clubs and museums. These experiences touch large numbers of people throughout their lifetimes. If you would like to share your research with the public, ISE can be an effective conduit for meaningful science communication. However, because the ISE field is so diverse, it can be overwhelming with its multiple entry points. If you already are part of an ISE initiative, knowing how to access the most useful resources easily can also be daunting. CAISE, the Center for Advancement of Informal Science Education, is a resource center for the ISE field funded by the National Science Foundation (NSF). CAISE can help connect you to the knowledge and people of ISE, through its website, products and in-person convenings. The proposed CAISE presentation will outline the diversity of the field and concisely present data that will make the case for the impact of ISE. We will focus on examples of successful programs that connect science with the public and that bring together AAS's science research community with practitioners and researchers within ISE. Pathways to various ISE resources in the form of current CAISE initiatives will be described as well. The presentation will include an interview section in which a CAISE staff member will ask questions of a scientist involved in an ISE initiative in order to detail one example of how ISE can be a valuable tool for engaging the public in science. Time for audience Q&A also will be included in the session.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A +B →0

NASA Astrophysics Data System (ADS)

Khandkar, Mahendra D.; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A ) and <> (B ). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A +B →0 , quite different from the A +A →0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A +A →0 . In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t-1/2, the fraction of persistent arrowheads decays as t-θ where θ is close to 1/4 , quite different from the Ising value. The global persistence too has θ =1/4 , as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

Coarsening and persistence in a one-dimensional system of orienting arrowheads: Domain-wall kinetics with A+B→0.

PubMed

Khandkar, Mahendra D; Stinchcombe, Robin; Barma, Mustansir

2017-01-01

We demonstrate the large-scale effects of the interplay between shape and hard-core interactions in a system with left- and right-pointing arrowheads <> on a line, with reorientation dynamics. This interplay leads to the formation of two types of domain walls, >< (A) and <> (B). The correlation length in the equilibrium state diverges exponentially with increasing arrowhead density, with an ordered state of like orientations arising in the limit. In this high-density limit, the A domain walls diffuse, while the B walls are static. In time, the approach to the ordered state is described by a coarsening process governed by the kinetics of domain-wall annihilation A+B→0, quite different from the A+A→0 kinetics pertinent to the Glauber-Ising model. The survival probability of a finite set of walls is shown to decay exponentially with time, in contrast to the power-law decay known for A+A→0. In the thermodynamic limit with a finite density of walls, coarsening as a function of time t is studied by simulation. While the number of walls falls as t^{-1/2}, the fraction of persistent arrowheads decays as t^{-θ} where θ is close to 1/4, quite different from the Ising value. The global persistence too has θ=1/4, as follows from a heuristic argument. In a generalization where the B walls diffuse slowly, θ varies continuously, increasing with increasing diffusion constant.

Radiative corrections to the quark masses in the ferromagnetic Ising and Potts field theories

NASA Astrophysics Data System (ADS)

Rutkevich, Sergei B.

2017-10-01

We consider the Ising Field Theory (IFT), and the 3-state Potts Field Theory (PFT), which describe the scaling limits of the two-dimensional lattice q-state Potts model with q = 2, and q = 3, respectively. At zero magnetic field h = 0, both field theories are integrable away from the critical point, have q degenerate vacua in the ferromagnetic phase, and q (q - 1) particles of the same mass - the kinks interpolating between two different vacua. Application of a weak magnetic field induces confinement of kinks into bound states - the "mesons" (for q = 2 , 3) consisting predominantly of two kinks, and "baryons" (for q = 3), which are essentially the three-kink excitations. The kinks in the confinement regime are also called "the quarks". We review and refine the Form Factor Perturbation Theory (FFPT), adapting it to the analysis of the confinement problem in the limit of small h, and apply it to calculate the corrections to the kink (quark) masses induced by the multi-kink fluctuations caused by the weak magnetic field. It is shown that the subleading third-order ∼h3 correction to the kink mass vanishes in the IFT. The leading second order ∼h2 correction to the kink mass in the 3-state PFT is estimated by truncation the infinite form factor expansion at the first term representing contribution of the two-kink fluctuations into the kink self-energy.

Glaubers Ising chain between two thermostats

NASA Astrophysics Data System (ADS)

Cornu, F.; Hilhorst, H. J.

2017-04-01

We consider a one-dimensional Ising model with N spins, each in contact with two thermostats of distinct temperatures, T 1 and T 2. Under Glauber dynamics the stationary state happens to coincide with the equilibrium state at an effective intermediate temperature T≤ft({{T}1},{{T}2}\\right) . The system nevertheless carries a nontrivial energy current between the thermostats. By means of the fermionization technique, for a chain initially in equilibrium at an arbitrary temperature T 0 we calculate the Fourier transform of the probability P≤ft(Q;τ \\right) for the time-integrated energy current Q during a finite time interval τ. In the long time limit we determine the corresponding generating function for the cumulants per site and unit of time, {< {{Q}n}>\\text{c}}/(Nτ ) , and explicitly give those with n  =  1, 2, 3, 4. We exhibit various phenomena in specific regimes: kinetic mean-field effects when one thermostat flips any spin less often than the other one, as well as dissipation towards a thermostat at zero temperature. Moreover, when the system size N goes to infinity while the effective temperature T vanishes, the cumulants of Q per unit of time grow linearly with N and are equal to those of a random walk process. In two adequate scaling regimes involving T and N we exhibit the dependence of the first correction upon the ratio of the spin-spin correlation length ξ (T) and the size N.

ISE: An Integrated Search Environment. The manual

NASA Technical Reports Server (NTRS)

Chu, Lon-Chan

1992-01-01

Integrated Search Environment (ISE), a software package that implements hierarchical searches with meta-control, is described in this manual. ISE is a collection of problem-independent routines to support solving searches. Mainly, these routines are core routines for solving a search problem and they handle the control of searches and maintain the statistics related to searches. By separating the problem-dependent and problem-independent components in ISE, new search methods based on a combination of existing methods can be developed by coding a single master control program. Further, new applications solved by searches can be developed by coding the problem-dependent parts and reusing the problem-independent parts already developed. Potential users of ISE are designers of new application solvers and new search algorithms, and users of experimental application solvers and search algorithms. The ISE is designed to be user-friendly and information rich. In this manual, the organization of ISE is described and several experiments carried out on ISE are also described.

Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

PubMed Central

Ribeiro, Haroldo V.; Zunino, Luciano; Lenzi, Ervin K.; Santoro, Perseu A.; Mendes, Renio S.

2012-01-01

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable. PMID:22916097

One-dimensional ferromagnetic array compound [Co3(SBA)2(OH)2(H2O)2]n, (SBA = 4-sulfobenzoate)

NASA Astrophysics Data System (ADS)

Honda, Zentaro; Nomoto, Naoyuki; Fujihara, Takashi; Hagiwara, Masayuki; Kida, Takanori; Sawada, Yuya; Fukuda, Takeshi; Kamata, Norihiko

2018-06-01

We report on the syntheses, crystal structure, and magnetic properties of the transition metal coordination polymer [Co3(SBA)2(OH)2(H2O)2]n, (SBA = 4-sulfobenzoate) in which CoO6 octahedra are linked through their edges, forming one-dimensional (1D) Co(II) arrays running along the crystal a-axis. These arrays are further perpendicularly bridged by SBA ligand to construct a three-dimensional framework. Its magnetic properties have been investigated, and ferromagnetic interactions within the arrays have been found. From heat capacity measurements, we have found that this compound exhibits a three-dimensional ferromagnetic phase transition at TC = 1.54 K, and the specific heat just above TC shows a Schottky anomaly which originates from an energy gap caused by uniaxial magnetic anisotropy. These results suggest that [Co3(SBA)2(OH)2(H2O)2]n consists of weakly coupled 1D ferromagnetic Ising arrays.

Quantum gravity as an information network self-organization of a 4D universe

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-10-01

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point, while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without a big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension.

Finite size induces crossover temperature in growing spin chains

NASA Astrophysics Data System (ADS)

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A.

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Finite size induces crossover temperature in growing spin chains.

PubMed

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

PubMed Central

Chiesa, Alessandro; Santini, Paolo; Gerace, Dario; Raftery, James; Houck, Andrew A.; Carretta, Stefano

2015-01-01

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence. PMID:26563516

String order parameters for one-dimensional Floquet symmetry protected topological phases

NASA Astrophysics Data System (ADS)

Kumar, Ajesh; Dumitrescu, Philipp T.; Potter, Andrew C.

2018-06-01

Floquet symmetry protected topological (FSPT) phases are nonequilibrium topological phases enabled by time-periodic driving. FSPT phases of one-dimensional (1D) chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum information without decoherence, making them promising for use as quantum memories. While FSPT order cannot be detected by any local measurement, here we construct nonlocal string order parameters that directly measure general 1D FSPT order. We propose a superconducting-qubit array based realization of the simplest Ising FSPT phase, which can be implemented with existing quantum computing hardware. We devise an interferometric scheme to directly measure the nonlocal string order using only simple one- and two-qubit operations and single-qubit measurements.

The application of dimensional analysis to the problem of solar wind-magnetosphere energy coupling

NASA Technical Reports Server (NTRS)

Bargatze, L. F.; Mcpherron, R. L.; Baker, D. N.; Hones, E. W., Jr.

1984-01-01

The constraints imposed by dimensional analysis are used to find how the solar wind-magnetosphere energy transfer rate depends upon interplanetary parameters. The analyses assume that only magnetohydrodynamic processes are important in controlling the rate of energy transfer. The study utilizes ISEE-3 solar wind observations, the AE index, and UT from three 10-day intervals during the International Magnetospheric Study. Simple linear regression and histogram techniques are used to find the value of the magnetohydrodynamic coupling exponent, alpha, which is consistent with observations of magnetospheric response. Once alpha is estimated, the form of the solar wind energy transfer rate is obtained by substitution into an equation of the interplanetary variables whose exponents depend upon alpha.

Large-Scale Simulation of Multi-Asset Ising Financial Markets

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2017-03-01

We perform a large-scale simulation of an Ising-based financial market model that includes 300 asset time series. The financial system simulated by the model shows a fat-tailed return distribution and volatility clustering and exhibits unstable periods indicated by the volatility index measured as the average of absolute-returns. Moreover, we determine that the cumulative risk fraction, which measures the system risk, changes at high volatility periods. We also calculate the inverse participation ratio (IPR) and its higher-power version, IPR6, from the absolute-return cross-correlation matrix. Finally, we show that the IPR and IPR6 also change at high volatility periods.

Simulation of financial market via nonlinear Ising model

NASA Astrophysics Data System (ADS)

Ko, Bonggyun; Song, Jae Wook; Chang, Woojin

2016-09-01

In this research, we propose a practical method for simulating the financial return series whose distribution has a specific heaviness. We employ the Ising model for generating financial return series to be analogous to those of the real series. The similarity between real financial return series and simulated one is statistically verified based on their stylized facts including the power law behavior of tail distribution. We also suggest the scheme for setting the parameters in order to simulate the financial return series with specific tail behavior. The simulation method introduced in this paper is expected to be applied to the other financial products whose price return distribution is fat-tailed.

Magnetization of the Ising model on the Sierpinski pastry-shell

NASA Astrophysics Data System (ADS)

Chame, Anna; Branco, N. S.

1992-02-01

Using a real-space renormalization group approach, we calculate the approximate magnetization in the Ising model on the Sierpinski Pastry-shell. We consider, as an approximation, only two regions of the fractal: the internal surfaces, or walls (sites on the border of eliminated areas), with coupling constants JS, and the bulk (all other sites), with coupling constants Jv. We obtain the mean magnetization of the two regions as a function of temperature, for different values of α= JS/ JV and different geometric parameters b and l. Curves present a step-like behavior for some values of b and l, as well as different universality classes for the bulk transition.

Persistence of opinion in the Sznajd consensus model: computer simulation

NASA Astrophysics Data System (ADS)

Stauffer, D.; de Oliveira, P. M. C.

2002-12-01

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/t^θ. We find θ simeq 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising θ. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding.

Experimental linear-optics simulation of ground-state of an Ising spin chain.

PubMed

Xue, Peng; Zhan, Xian; Bian, Zhihao

2017-05-19

We experimentally demonstrate a photonic quantum simulator: by using a two-spin Ising chain (an isolated dimer) as an example, we encode the wavefunction of the ground state with a pair of entangled photons. The effect of magnetic fields, leading to a critical modification of the correlation between two spins, can be simulated by just local operations. With the ratio of simulated magnetic fields and coupling strength increasing, the ground state of the system changes from a product state to an entangled state and back to another product state. The simulated ground states can be distinguished and the transformations between them can be observed by measuring correlations between photons. This simulation of the Ising model with linear quantum optics opens the door to the future studies which connect quantum information and condensed matter physics.

Evidence for single-chain magnet behavior in a Mn(III)-Ni(II) chain designed with high spin magnetic units: a route to high temperature metastable magnets.

PubMed

Clérac, Rodolphe; Miyasaka, Hitoshi; Yamashita, Masahiro; Coulon, Claude

2002-10-30

We herein present the synthesis, crystal structure, and magnetic properties of a new heterometallic chain of MnIII and NiII ions, [Mn2(saltmen)2Ni(pao)2(py)2](ClO4)2 (1) (saltmen2- = N,N'-(1,1,2,2-tetramethylethylene) bis(salicylideneiminate) and pao- = pyridine-2-aldoximate). The crystal structure of 1 was investigated by X-ray crystallographic analysis: compound 1 crystallized in monoclinic, space group C2/c (No. 15) with a = 21.140(3) A, b = 15.975(1) A, c = 18.6212(4) A, beta = 98.0586(4) degrees , V = 6226.5(7) A3, and Z = 4. This compound consists of two fragments, the out-of-plane dimer [Mn2(saltmen)2]2+ as a coordination acceptor building block and the neutral mononuclear unit [Ni(pao)2(py)2] as a coordination donor building block, forming an alternating chain having the repeating unit [-Mn-(O)2-Mn-ON-Ni-NO-]n. In the crystal structure, each chain is well separated with a minimum intermetallic distance between Mn and Ni ions of 10.39 A and with the absence of interchain pi overlaps between organic ligands. These features ensure a good magnetic isolation of the chains. The dc and ac magnetic measurements were performed on both the polycrystalline sample and the aligned single crystals of 1. Above 30 K, the magnetic susceptibility of this one-dimensional compound was successfully described in a mean field approximation as an assembly of trimers (Mn...Ni...Mn) with a NiII...MnIII antiferromagnetic interaction (J = -21 K) connected through a ferromagnetic MnIII...MnIII interaction (J'). However, the mean field theory fails to describe the magnetic behavior below 30 K emphasizing the one-dimensional magnetic character of the title compound. Between 5 and 15 K, the susceptibility in the chain direction was fitted to a one-dimensional Ising model leading to the same value of J'. Hysteresis loops are observed below 3.5 K, indicating a magnet-type behavior. In the same range of temperature, combined ac and dc measurements show a slow relaxation of the magnetization. This result indicates the presence of a metastable state without magnetic long-range order. This material is the first experimental design of a heterometallic chain with ST = 3 magnetic units showing a "single-chain magnet" behavior predicted in 1963 by R. J. Glauber for an Ising one-dimensional system. This work opens new perspectives for one-dimensional systems to obtain high temperature metastable magnets by combining high spin magnetic units, strong interunit interactions, and uniaxial anisotropy.

Network of time-multiplexed optical parametric oscillators as a coherent Ising machine

NASA Astrophysics Data System (ADS)

Marandi, Alireza; Wang, Zhe; Takata, Kenta; Byer, Robert L.; Yamamoto, Yoshihisa

2014-12-01

Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. Here, we report an Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programmed a small non-deterministic polynomial time-hard problem on a 4-OPO Ising machine and in 1,000 runs no computational error was detected.

Universal Features of Left-Right Entanglement Entropy.

PubMed

Das, Diptarka; Datta, Shouvik

2015-09-25

We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.

Aptamer cell sensor based on porous graphene oxide decorated ion-selective-electrode: Double sensing platform for cell and ion.

PubMed

Zhang, Rong; Gu, Yajun; Wang, Zhongrong; Li, Yueguo; Fan, Qingjie; Jia, Yunfang

2018-06-15

Enlightened by the emerging cell-ion detection based on ion-selective-electrode (ISE), an aptamer capturing and ISE transducing (AC&IT) strategy is proposed on the porous graphene oxide (PGO) decorated ISE (PGO-ISE), its performances in both cell and ion detections are examined by use of AS1411 targeted A549 cell detection and iodide-ISE as proof-of-concept. Firstly, GO flakes, exfoliated from graphite by modified Hummers method, are cross-linked by thiourea mediated hydrothermal process, to 3-dimension networked PGO which is identified by scanning-electron-microscope, UV-visible absorbance and X-ray photoelectron spectroscopy; its enhancing effect for cell capturing is evaluated by microscopy. Then, PGO-ISE is constructed by drop-coating PGO film on the surface of ISE and followed by covalently anchoring AS1411. Electrochemistry measurements for different state ISE (blank, PGO coated, AS1411 anchored and A549 captured) are performed by our home-made ISE-measuring system. It is demonstrated that the best cell-sensitivity in buffer is - 25.21 mV/log 10 C A549 (R 2 = 0.91), resolution in blood is 10 cells/ml. Interestingly, due to PGO's scaffold protection to the ionophore, I - -sensitivity is preserved as - 42.98 mV/pI (R 2 = 0.95, pI = -log 10 (C I )). Theoretical explanations are provided for the double-sensing phenomenon according to basic ISE principle. It is believed the PGO-ISE based aptamer cell sensor will be a promising experimental means for biomedical researches. Copyright © 2018. Published by Elsevier B.V.

A Resource Center for Informal Science Education

NASA Astrophysics Data System (ADS)

Dickow, B.

2011-12-01

Informal science education (ISE) is playing an increasingly important role in how and where the public engages with science. A growing body of research is showing that people learn the majority of their science knowledge outside of school (Falk & Dierking, 2010). The ISE field includes a wide variety of sources, including the internet, TV programs, magazines, hobby clubs and museums, all sectors of the informal science education field. These experiences touch large numbers of people throughout their lifetimes. If you would like to share your research with the public, ISE can be an effective conduit for meaningful science communication. However, because the ISE field is so diverse, it can be overwhelming with its multiple entry points. If you already are part of an ISE initiative, knowing how to access the most useful resources easily can also be daunting. CAISE, the Center for Advancement of Informal Science Education, is a resource center for the ISE field funded by the National Science Foundation (NSF). CAISE can help connect you to the knowledge and people of ISE, through its website, products and in-person convenings. The proposed CAISE presentation will outline the diversity of the field and concisely present data that will make the case for the impact of ISE. We will focus on examples of successful programs that connect science with the public and that bring together AGU's science research community with practitioners and researchers within ISE. Pathways to various ISE resources in the form of current CAISE initiatives will be described as well. The presentation will include an interview section in which a CAISE staff member will ask questions of a scientist involved in an ISE initiative in order to detail one example of how ISE can be a valuable tool for engaging the public in science. Time for audience Q&A also will be included in the session.

Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach.

PubMed

Barradas-Bautista, Didier; Alvarado-Mentado, Matias; Agostino, Mark; Cocho, Germinal

2018-01-01

This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense.

A study of the temporal and spectral characteristics of gamma ray bursts. Ph.D. Thesis - Maryland Univ.

NASA Technical Reports Server (NTRS)

Norris, J.

1983-01-01

Gamma-ray burst data obtained from the ISEE-3 Gamma Ray Burst Spectrometer and the Solar Maximum Mission's Hard X-ray Burst Spectrometer (HXRBS) were analyzed to yield information on burst temporal and spectral characteristics. A Monte Carlo approach was used to simulate the HXRBS response to candidate spectral models. At energies above about 100 keV, the spectra are well fit by exponential forms. At lower energies, 30 keV to 60 keV, depressions below the model continua are apparent in some bursts. The depressions are not instrumental or data-reduction artifacts. The event selection criterion of the ISEE-3 experiment is based on the time to accumulate a present number of photons rather than the photon count per unit time and is consequently independent of event duration for a given burst intensity, unlike most conventional systems. As a result, a significantly greater percentage of fast, narrow events have been detected. The ratio of count rates from two ISEE-3 detectors indicates that bursts with durations or approx. one second have much softer spectra than longer bursts.

Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

NASA Astrophysics Data System (ADS)

Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.

2014-01-01

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.

The role of explicit and implicit self-esteem in peer modeling of palatable food intake: a study on social media interaction among youngsters.

PubMed

Bevelander, Kirsten E; Anschütz, Doeschka J; Creemers, Daan H M; Kleinjan, Marloes; Engels, Rutger C M E

2013-01-01

This experimental study investigated the impact of peers on palatable food intake of youngsters within a social media setting. To determine whether this effect was moderated by self-esteem, the present study examined the roles of global explicit self-esteem (ESE), body esteem (BE) and implicit self-esteem (ISE). Participants (N = 118; 38.1% boys; M age 11.14±.79) were asked to play a computer game while they believed to interact online with a same-sex normal-weight remote confederate (i.e., instructed peer) who ate either nothing, a small or large amount of candy. Participants modeled the candy intake of peers via a social media interaction, but this was qualified by their self-esteem. Participants with higher ISE adjusted their candy intake to that of a peer more closely than those with lower ISE when the confederate ate nothing compared to when eating a modest (β = .26, p = .05) or considerable amount of candy (kcal) (β = .32, p = .001). In contrast, participants with lower BE modeled peer intake more than those with higher BE when eating nothing compared to a considerable amount of candy (kcal) (β = .21, p = .02); ESE did not moderate social modeling behavior. In addition, participants with higher discrepant or "damaged" self-esteem (i.e., high ISE and low ESE) modeled peer intake more when the peer ate nothing or a modest amount compared to a substantial amount of candy (kcal) (β = -.24, p = .004; β = -.26, p<.0001, respectively). Youngsters conform to the amount of palatable food eaten by peers through social media interaction. Those with lower body esteem or damaged self-esteem may be more at risk to peer influences on food intake.

The Role of Explicit and Implicit Self-Esteem in Peer Modeling of Palatable Food Intake: A Study on Social Media Interaction among Youngsters

PubMed Central

Bevelander, Kirsten E.; Anschütz, Doeschka J.; Creemers, Daan H. M.; Kleinjan, Marloes; Engels, Rutger C. M. E.

2013-01-01

Objective This experimental study investigated the impact of peers on palatable food intake of youngsters within a social media setting. To determine whether this effect was moderated by self-esteem, the present study examined the roles of global explicit self-esteem (ESE), body esteem (BE) and implicit self-esteem (ISE). Methods Participants (N = 118; 38.1% boys; M age 11.14±.79) were asked to play a computer game while they believed to interact online with a same-sex normal-weight remote confederate (i.e., instructed peer) who ate either nothing, a small or large amount of candy. Results Participants modeled the candy intake of peers via a social media interaction, but this was qualified by their self-esteem. Participants with higher ISE adjusted their candy intake to that of a peer more closely than those with lower ISE when the confederate ate nothing compared to when eating a modest (β = .26, p = .05) or considerable amount of candy (kcal) (β = .32, p = .001). In contrast, participants with lower BE modeled peer intake more than those with higher BE when eating nothing compared to a considerable amount of candy (kcal) (β = .21, p = .02); ESE did not moderate social modeling behavior. In addition, participants with higher discrepant or “damaged” self-esteem (i.e., high ISE and low ESE) modeled peer intake more when the peer ate nothing or a modest amount compared to a substantial amount of candy (kcal) (β = −.24, p = .004; β = −.26, p<.0001, respectively). Conclusion Youngsters conform to the amount of palatable food eaten by peers through social media interaction. Those with lower body esteem or damaged self-esteem may be more at risk to peer influences on food intake. PMID:24015251

I. Excluded volume effects in Ising cluster distributions and nuclear multifragmentation. II. Multiple-chance effects in alpha-particle evaporation

NASA Astrophysics Data System (ADS)

Breus, Dimitry Eugene

In Part I, geometric clusters of the Ising model are studied as possible model clusters for nuclear multifragmentation. These clusters may not be considered as non-interacting (ideal gas) due to excluded volume effect which predominantly is the artifact of the cluster's finite size. Interaction significantly complicates the use of clusters in the analysis of thermodynamic systems. Stillinger's theory is used as a basis for the analysis, which within the RFL (Reiss, Frisch, Lebowitz) fluid-of-spheres approximation produces a prediction for cluster concentrations well obeyed by geometric clusters of the Ising model. If thermodynamic condition of phase coexistence is met, these concentrations can be incorporated into a differential equation procedure of moderate complexity to elucidate the liquid-vapor phase diagram of the system with cluster interaction included. The drawback of increased complexity is outweighted by the reward of greater accuracy of the phase diagram, as it is demonstrated by the Ising model. A novel nuclear-cluster analysis procedure is developed by modifying Fisher's model to contain cluster interaction and employing the differential equation procedure to obtain thermodynamic variables. With this procedure applied to geometric clusters, the guidelines are developed to look for excluded volume effect in nuclear multifragmentation. In Part II, an explanation is offered for the recently observed oscillations in the energy spectra of alpha-particles emitted from hot compound nuclei. Contrary to what was previously expected, the oscillations are assumed to be caused by the multiple-chance nature of alpha-evaporation. In a semi-empirical fashion this assumption is successfully confirmed by a technique of two-spectra decomposition which treats experimental alpha-spectra as having contributions from at least two independent emitters. Building upon the success of the multiple-chance explanation of the oscillations, Moretto's single-chance evaporation theory is augmented to include multiple-chance emission and tested on experimental data to yield positive results.

Transverse fields to tune an Ising-nematic quantum phase transition

NASA Astrophysics Data System (ADS)

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.; Berg, Erez; Fernandes, Rafael M.; Fisher, Ian R.; Kivelson, Steven A.

2017-12-01

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

77 FR 61037 - Self-Regulatory Organizations; International Securities Exchange, LLC; Notice of Filing and...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-05

... Rule Change To Adopt Reduced Fees for Historical ISE Open/Close Trade Profile Intraday Market Data... historical ISE Open/Close Trade Profile Intraday market data offering. The text of the proposed rule change... Change 1. Purpose ISE currently sells the ISE Open/Close Trade Profile Intraday, a market data offering...

Substorms, Plasmoids, Flux Robes, and Magnetotail Flux Loss on March 25, 1983: CDAW-8

DTIC Science & Technology

1988-10-03

1400 UT. The magnitude and orientation of the 11 GOES 5 OR 1982-01 9A SE14 14 ZSM -l1ORe ISEE 3 -10 -5 5 OReYSM YS m ISEE 1 5 14r- -* IMP 8 0 Fig. lb...and references therein]. ISEE 1 saw a 31% field decrease from 55 nT to 38 nT between 1020 and 1058 UT, and a 35 % decrease from 62 nT to 41 nT between...strength is determined by the component 29 2.5 POLAR CAP AREA 2.0 E ISEE 1 . 5 -i 60 x - 50 IMP 8 - 40 35 ISEE-3 (B = 22nt) 30 25 ISE IMP8 cc" Z u

Field dependence of the magnetic correlations of the frustrated magnet SrDy 2 O 4

DOE PAGES

Gauthier, N.; Fennell, A.; Prévost, B.; ...

2017-05-30

Tmore » he frustrated magnet SrDy 2 O 4 exhibits a field-induced phase with a magnetization plateau at 1 / 3 of the saturation value for magnetic fields applied along the b axis. We report here a neutron scattering study of the nature and symmetry of the magnetic order in this field-induced phase. Below ≈ 0.5 K, there are strong hysteretic effects, and the order is short- or long-ranged for zero-field and field cooling, respectively. We find that the long-range ordered magnetic structure within the zigzag chains is identical to that expected for the one-dimensional axial next-nearest neighbor Ising (ANNNI) model in longitudinal fields. he long-range ordered structure in field contrasts with the short-range order found at zero field, and is most likely reached through enhanced quantum fluctuations with increasing fields.« less

Massively parallel multicanonical simulations

NASA Astrophysics Data System (ADS)

Gross, Jonathan; Zierenberg, Johannes; Weigel, Martin; Janke, Wolfhard

2018-03-01

Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged free-energy landscapes. As Markov chain methods, they are inherently serial computationally. It was demonstrated recently, however, that a combination of independent simulations that communicate weight updates at variable intervals allows for the efficient utilization of parallel computational resources for multicanonical simulations. Implementing this approach for the many-thread architecture provided by current generations of graphics processing units (GPUs), we show how it can be efficiently employed with of the order of 104 parallel walkers and beyond, thus constituting a versatile tool for Monte Carlo simulations in the era of massively parallel computing. We provide the fully documented source code for the approach applied to the paradigmatic example of the two-dimensional Ising model as starting point and reference for practitioners in the field.

Correlated lateral phase separations in stacks of lipid membranes

NASA Astrophysics Data System (ADS)

Hoshino, Takuma; Komura, Shigeyuki; Andelman, David

2015-12-01

Motivated by the experimental study of Tayebi et al. [Nat. Mater. 11, 1074 (2012)] on phase separation of stacked multi-component lipid bilayers, we propose a model composed of stacked two-dimensional Ising spins. We study both its static and dynamical features using Monte Carlo simulations with Kawasaki spin exchange dynamics that conserves the order parameter. We show that at thermodynamical equilibrium, due to strong inter-layer correlations, the system forms a continuous columnar structure for any finite interaction across adjacent layers. Furthermore, the phase separation shows a faster dynamics as the inter-layer interaction is increased. This temporal behavior is mainly due to an effective deeper temperature quench because of the larger value of the critical temperature, Tc, for larger inter-layer interaction. When the temperature ratio, T/Tc, is kept fixed, the temporal growth exponent does not increase and even slightly decreases as a function of the increased inter-layer interaction.

Spontaneous structural distortion of the metallic Shastry-Sutherland system Dy B4 by quadrupole-spin-lattice coupling

NASA Astrophysics Data System (ADS)

Sim, Hasung; Lee, Seongsu; Hong, Kun-Pyo; Jeong, Jaehong; Zhang, J. R.; Kamiyama, T.; Adroja, D. T.; Murray, C. A.; Thompson, S. P.; Iga, F.; Ji, S.; Khomskii, D.; Park, Je-Geun

2016-11-01

Dy B4 has a two-dimensional Shastry-Sutherland (Sh-S) lattice with strong Ising character of the Dy ions. Despite the intrinsic frustrations, it undergoes two successive transitions: a magnetic ordering at TN=20 K and a quadrupole ordering at TQ=12.5 K . From high-resolution neutron and synchrotron x-ray powder diffraction studies, we have obtained full structural information on this material in all phases and demonstrate that structural modifications occurring at quadrupolar transition lead to the lifting of frustrations inherent in the Sh-S model. Our paper thus provides a complete experimental picture of how the intrinsic frustration of the Sh-S lattice can be lifted by the coupling to quadrupole moments. We show that two other factors, i.e., strong spin-orbit coupling and long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in metallic Dy B4 , play an important role in this behavior.

Bootstrapping conformal field theories with the extremal functional method.

PubMed

El-Showk, Sheer; Paulos, Miguel F

2013-12-13

The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and operator product expansion (OPE) coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the extremal functional method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the two-dimensional Ising model based solely on the dimension of a single scalar quasiprimary--no Virasoro algebra required. Our work serves as a benchmark for applications to more interesting, less known CFTs in the near future.

The effect of surface and interface on Neel transition temperature of low-dimensional antiferromagnetic materials

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

Zhang, Wen; Zhou, Zhaofeng, E-mail: zfzhou@xtu.edu.cn; Zhong, Yuan

2015-11-15

Incorporating the bond order-length-strength (BOLS) notion with the Ising premise, we have modeled the size dependence of the Neel transition temperature (T{sub N}) of antiferromagnetic nanomaterials. Reproduction of the size trends reveals that surface atomic undercoordination induces bond contraction, and interfacial hetero-coordination induces bond nature alteration. Both surface and interface of nanomaterials modulate the T{sub N} by adjusting the atomic cohesive energy. The T{sub N} is related to the atomic cohesive/exchange energy that is lowered by the coordination number (CN) imperfection of the undercoordinated atoms near the surface and altered by the changed bond nature of epitaxial interface. A numericalmore » match between predictions and measurements reveals that the T{sub N} of antiferromagnetic nanomaterials declines with reduced size and increases with both the strengthening of heterogeneous bond and the increase of the bond number.« less

Field dependence of the magnetic correlations of the frustrated magnet SrDy2O4

NASA Astrophysics Data System (ADS)

Gauthier, N.; Fennell, A.; Prévost, B.; Désilets-Benoit, A.; Dabkowska, H. A.; Zaharko, O.; Frontzek, M.; Sibille, R.; Bianchi, A. D.; Kenzelmann, M.

2017-05-01

The frustrated magnet SrDy2O4 exhibits a field-induced phase with a magnetization plateau at 1 /3 of the saturation value for magnetic fields applied along the b axis. We report here a neutron scattering study of the nature and symmetry of the magnetic order in this field-induced phase. Below T ≈0.5 K, there are strong hysteretic effects, and the order is short- or long-ranged for zero-field and field cooling, respectively. We find that the long-range ordered magnetic structure within the zigzag chains is identical to that expected for the one-dimensional axial next-nearest neighbor Ising (ANNNI) model in longitudinal fields. The long-range ordered structure in field contrasts with the short-range order found at zero field, and is probably reached through enhanced quantum fluctuations with increasing fields.

A pentacene monolayer trapped between graphene and a substrate.

PubMed

Zhang, Qicheng; Peng, Boyu; Chan, Paddy Kwok Leung; Luo, Zhengtang

2015-09-21

A self-assembled pentacene monolayer can be fabricated between the solid-solid interface of few-layered graphene (FLG) and the mica substrate, through a diffusion-spreading method. By utilizing a transfer method that allows us to sandwich pentacene between graphene and mica, followed by controlled annealing, we enabled the diffused pentacene to be trapped in the interfaces and led to the formation of a stable monolayer. We found that the formation of a monolayer is kinetically favored by using a 2D Ising lattice gas model for pentacene trapped between the graphene-substrate interfaces. This kinetic Monte Carlo simulation results indicate that, due to the graphene substrate enclosure, the spreading of the first layer proceeds faster than the second layer, as the kinetics favors the filling of voids by molecules from the second layer. This graphene assisted monolayer assembly method provides a new avenue for the fabrication of two-dimensional monolayer structures.

Prethermalization and persistent order in the absence of a thermal phase transition

NASA Astrophysics Data System (ADS)

Halimeh, Jad C.; Zauner-Stauber, Valentin; McCulloch, Ian P.; de Vega, Inés; Schollwöck, Ulrich; Kastner, Michael

2017-01-01

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions (∝1 /rα with distance r ), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of α for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on α as well as on the quench parameters.

Highly anisotropic exchange interactions of j eff = 1 2 iridium moments on the fcc lattice in La 2 B IrO 6   ( B = Mg , Zn )

DOE PAGES

Aczel, A. A.; Cook, A. M.; Williams, T. J.; ...

2016-06-20

Here we have performed inelastic neutron scattering (INS) experiments to investigate the magnetic excitations in the weakly distorted face-centered-cubic (fcc) iridate double perovskites Lamore » $$_2$$ZnIrO$$_6$$ and La$$_2$$MgIrO$$_6$$, which are characterized by A-type antiferromagnetic ground states. The powder inelastic neutron scattering data on these geometrically frustrated $$j_{\\rm eff}=1/2$$ Mott insulators provide clear evidence for gapped spin wave excitations with very weak dispersion. The INS results and thermodynamic data on these materials can be reproduced by conventional Heisenberg-Ising models with significant uniaxial Ising anisotropy and sizeable second-neighbor ferromagnetic interactions. Such a uniaxial Ising exchange interaction is symmetry-forbidden on the ideal fcc lattice, so that it can only arise from the weak crystal distortions away from the ideal fcc limit. This may suggest that even weak distortions in $$j_{\\rm eff}=1/2$$ Mott insulators might lead to strong exchange anisotropies. More tantalizingly, however, we find an alternative viable explanation of the INS results in terms of spin models with a dominant Kitaev interaction. In contrast to the uniaxial Ising exchange, the highly-directional Kitaev interaction is a type of exchange anisotropy which is symmetry-allowed even on the ideal fcc lattice. The Kitaev model has a magnon gap induced by quantum order-by-disorder, while weak anisotropies of the Kitaev couplings generated by the symmetry-lowering due to lattice distortions can pin the order and enhance the magnon gap. In conclusion, our findings highlight how even conventional magnetic orders in heavy transition metal oxides may be driven by highly-directional exchange interactions rooted in strong spin-orbit coupling.« less

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

NASA Astrophysics Data System (ADS)

Prisk, T. R.; Hoffmann, C.; Kolesnikov, A. I.; Mamontov, E.; Podlesnyak, A. A.; Wang, X.; Kent, P. R. C.; Anovitz, L. M.

2018-05-01

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factor reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10-100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

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

Prisk, Timothy; Hoffmann, Christina; Kolesnikov, Alexander I.

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here in this paper, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factormore » reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10–100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.« less

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

DOE PAGES

Prisk, Timothy; Hoffmann, Christina; Kolesnikov, Alexander I.; ...

2018-05-09

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here in this paper, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factormore » reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10–100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.« less

Ising lattices with +/-J second-nearest-neighbor interactions

NASA Astrophysics Data System (ADS)

Ramírez-Pastor, A. J.; Nieto, F.; Vogel, E. E.

1997-06-01

Second-nearest-neighbor interactions are added to the usual nearest-neighbor Ising Hamiltonian for square lattices in different ways. The starting point is a square lattice where half the nearest-neighbor interactions are ferromagnetic and the other half of the bonds are antiferromagnetic. Then, second-nearest-neighbor interactions can also be assigned randomly or in a variety of causal manners determined by the nearest-neighbor interactions. In the present paper we consider three causal and three random ways of assigning second-nearest-neighbor exchange interactions. Several ground-state properties are then calculated for each of these lattices:energy per bond ɛg, site correlation parameter pg, maximal magnetization μg, and fraction of unfrustrated bonds hg. A set of 500 samples is considered for each size N (number of spins) and array (way of distributing the N spins). The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.

A Meloidogyne incognita effector MiISE5 suppresses programmed cell death to promote parasitism in host plant.

PubMed

Shi, Qianqian; Mao, Zhenchuan; Zhang, Xi; Zhang, Xiaoping; Wang, Yunsheng; Ling, Jian; Lin, Runmao; Li, Denghui; Kang, Xincong; Sun, Wenxian; Xie, Bingyan

2018-05-08

Root-knot nematodes (RKNs) are highly specialized parasites that interact with their host plants using a range of strategies. The esophageal glands are the main places where nematodes synthesize effector proteins, which play central roles in successful invasion. The Meloidogyne incognita effector MiISE5 is exclusively expressed within the subventral esophageal cells and is upregulated during early parasitic stages. In this study, we show that MiISE5 can be secreted to barley cells through infectious hyphae of Magnaporthe oryzae. Transgenic Arabidopsis plants expressing MiISE5 became significantly more susceptible to M. incognita. Inversely, the tobacco rattle virus (TRV)-mediated silence of MiISE5 decreased nematode parasitism. Moreover, transient expression of MiISE5 suppressed cell death caused by Burkholderia glumae in Nicotiana benthamiana. Based on transcriptome analysis of MiISE5 transgenic sample and the wild-type (WT) sample, we obtained 261 DEGs, and the results of GO and KEGG enrichment analysis indicate that MiISE5 can interfere with various metabolic and signaling pathways, especially the JA signaling pathway, to facilitate nematode parasitism. Results from the present study suggest that MiISE5 plays an important role during the early stages of parasitism and provides evidence to decipher the molecular mechanisms underlying the manipulation of host immune defense responses by M. incognita.

75 FR 48734 - Self-Regulatory Organizations; EDGX Exchange, Inc.; Notice of Filing and Immediate Effectiveness...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-11

...) ISE FIX Session Fees The Exchange proposes to charge for legacy ISE \\4\\ Financial Information Exchange...-79). \\5\\ As stated in SR-ISE-2007-79, the ISE used the Financial Information Exchange (FIX) protocol... will provide Members a $0.0031 rebate per share for liquidity added on EDGX if the Member on a daily...

Emergent long-range synchronization of oscillating ecological populations without external forcing described by Ising universality

PubMed Central

Noble, Andrew E.; Machta, Jonathan; Hastings, Alan

2015-01-01

Understanding the synchronization of oscillations across space is fundamentally important to many scientific disciplines. In ecology, long-range synchronization of oscillations in spatial populations may elevate extinction risk and signal an impending catastrophe. The prevailing assumption is that synchronization on distances longer than the dispersal scale can only be due to environmental correlation (the Moran effect). In contrast, we show how long-range synchronization can emerge over distances much longer than the length scales of either dispersal or environmental correlation. In particular, we demonstrate that the transition from incoherence to long-range synchronization of two-cycle oscillations in noisy spatial population models is described by the Ising universality class of statistical physics. This result shows, in contrast to all previous work, how the Ising critical transition can emerge directly from the dynamics of ecological populations. PMID:25851364

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

NASA Astrophysics Data System (ADS)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Dendrimer-magnetic nanostructure: a Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Jabar, A.; Masrour, R.

2017-11-01

In this paper, the magnetic properties of ternary mixed spins (σ,S,q) Ising model on a dendrimer nanostructure are studied using Monte Carlo simulations. The ground state phase diagrams of dendrimer nanostructure with ternary mixed spins σ = 1/2, S = 1 and q = 3/2 Ising model are found. The variation of the thermal total and partial magnetizations with the different exchange interactions, the external magnetic fields and the crystal fields have been also studied. The reduced critical temperatures have been deduced. The magnetic hysteresis cycles have been discussed. In particular, the corresponding magnetic coercive filed values have been deduced. The multiples hysteresis cycles are found. The dendrimer nanostructure has several applications in the medicine.

Learning and inference in a nonequilibrium Ising model with hidden nodes.

PubMed

Dunn, Benjamin; Roudi, Yasser

2013-02-01

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

The ISEE-1 and ISEE-2 plasma wave investigation

NASA Technical Reports Server (NTRS)

Gurnett, D. A.; Scarf, F. L.; Fredricks, R. W.; Smith, E. J.

1978-01-01

The ISEE-1 and ISEE-2 plasma wave experiments are designed to provide basic information on wave-particle interactions in the earth's magnetosphere and in the solar wind. The ISEE-1 plasma wave instrument uses three electric dipole antennas with lengths of 215, 73.5 and 0.61 m for electric field measurements, and a triaxial search coil antenna for magnetic field measurements. The ISEE-2 instrument uses two electric dipole antennas with lengths of 30 and 0.61 m for electric field measurements and a single-axis search coil antenna for magnetic field measurements. The primary scientific objectives of the experiments are described, including the resolution of space-time relationships of plasma wave phenomena and VLBI studies. The instrumentation is described, with emphasis on the antennas and the electronics.

Evolutionary games combining two or three pair coordinations on a square lattice

NASA Astrophysics Data System (ADS)

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Research on Intelligent Synthesis Environments

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Lobeck, William E.

2002-01-01

Four research activities related to Intelligent Synthesis Environment (ISE) have been performed under this grant. The four activities are: 1) non-deterministic approaches that incorporate technologies such as intelligent software agents, visual simulations and other ISE technologies; 2) virtual labs that leverage modeling, simulation and information technologies to create an immersive, highly interactive virtual environment tailored to the needs of researchers and learners; 3) advanced learning modules that incorporate advanced instructional, user interface and intelligent agent technologies; and 4) assessment and continuous improvement of engineering team effectiveness in distributed collaborative environments.

Evolutionary games combining two or three pair coordinations on a square lattice.

PubMed

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Frustration and correlations in stacked triangular-lattice Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Burnell, F. J.; Chalker, J. T.

2015-12-01

We study multilayer triangular-lattice Ising antiferromagnets with interlayer interactions that are weak and frustrated in an abc stacking. By analyzing a coupled height model description of these systems, we show that they exhibit a classical spin liquid regime at low temperature, in which both intralayer and interlayer correlations are strong but there is no long-range order. Diffuse scattering in this regime is concentrated on a helix in reciprocal space, as observed for charge ordering in the materials LuFe2O4 and YbFe2O4 .

Research on Intelligent Synthesis Environments

NASA Astrophysics Data System (ADS)

Noor, Ahmed K.; Loftin, R. Bowen

2002-12-01

Four research activities related to Intelligent Synthesis Environment (ISE) have been performed under this grant. The four activities are: 1) non-deterministic approaches that incorporate technologies such as intelligent software agents, visual simulations and other ISE technologies; 2) virtual labs that leverage modeling, simulation and information technologies to create an immersive, highly interactive virtual environment tailored to the needs of researchers and learners; 3) advanced learning modules that incorporate advanced instructional, user interface and intelligent agent technologies; and 4) assessment and continuous improvement of engineering team effectiveness in distributed collaborative environments.

Finite size effects on the experimental observables of the Glauber model: a theoretical and experimental investigation

NASA Astrophysics Data System (ADS)

Vindigni, A.; Bogani, L.; Gatteschi, D.; Sessoli, R.; Rettori, A.; Novak, M. A.

2004-05-01

We investigate the relaxation time, τ, of a dilute Glauber kinetic Ising chain obtained by ac susceptibility and SQUID magnetometry on a Co(II)-organic radical Ising 1D ferrimagnet doped with Zn(II). Theoretically we predicted a crossover in the temperature-dependence of τ, when the average segment is of the same order of the correlation length. Comparing the experimental results with theory we conclude that in the investigted temperature range the correlation length exceeds the finite length also in the pure sample.

Thermodynamics of alternate Ising chains of spins 1 and 3/2 with dipolar, biquadratic, and single ion interactions

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

Fireman, E.C.; dos Santos, R.J.

1997-04-01

Within a recently developed extended decoration-transformation formalism we study the thermodynamic properties of a linear chain of alternate Ising {sigma}=1 and S=3/2 spins. We allow for different anisotropy fields on each subchain of different spins. For some range of the parameter space we show the existence of a crossover from a ferromagnetic to an antiferromagnetic-like behavior of the model, as explicitly captured in the susceptibility results. {copyright} {ital 1997 American Institute of Physics.}

Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

NASA Astrophysics Data System (ADS)

Antenucci, F.; Crisanti, A.; Leuzzi, L.

2014-07-01

The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

Spin-ice behavior of three-dimensional inverse opal-like magnetic structures: Micromagnetic simulations

NASA Astrophysics Data System (ADS)

Dubitskiy, I. S.; Syromyatnikov, A. V.; Grigoryeva, N. A.; Mistonov, A. A.; Sapoletova, N. A.; Grigoriev, S. V.

2017-11-01

We perform micromagnetic simulations of the magnetization distribution in inverse opal-like structures (IOLS) made from ferromagnetic materials (nickel and cobalt). It is shown that the unit cell of these complex structures, whose characteristic length is approximately 700 nm, can be divided into a set of structural elements some of which behave like Ising-like objects. A spin-ice behavior of IOLS is observed in a broad range of external magnetic fields. Numerical results describe successfully the experimental hysteresis curves of the magnetization in Ni- and Co-based IOLS. We conclude that ferromagnetic IOLS can be considered as the first realization of three-dimensional artificial spin ice. The problem is discussed of optimal geometrical properties and material characteristics of IOLS for the spin-ice rule fulfillment.

Cancer growth and metastasis as a metaphor of Go gaming: An Ising model approach

PubMed Central

Barradas-Bautista, Didier; Agostino, Mark; Cocho, Germinal

2018-01-01

This work aims for modeling and simulating the metastasis of cancer, via the analogy between the cancer process and the board game Go. In the game of Go, black stones that play first could correspond to a metaphor of the birth, growth, and metastasis of cancer. Moreover, playing white stones on the second turn could correspond the inhibition of cancer invasion. Mathematical modeling and algorithmic simulation of Go may therefore benefit the efforts to deploy therapies to surpass cancer illness by providing insight into the cellular growth and expansion over a tissue area. We use the Ising Hamiltonian, that models the energy exchange in interacting particles, for modeling the cancer dynamics. Parameters in the energy function refer the biochemical elements that induce cancer birth, growth, and metastasis; as well as the biochemical immune system process of defense. PMID:29718932

Relationship between the transverse-field Ising model and the X Y model via the rotating-wave approximation

NASA Astrophysics Data System (ADS)

Kiely, Thomas G.; Freericks, J. K.

2018-02-01

In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the X Y model in no field (when measurements are performed at the proper stroboscopic times). We describe the details for how this relationship works and, in particular, we also show under what circumstances it fails. We examine wave-function overlap between the two models and observables, such as spin-spin Green's functions. In general, the mapping is quite robust at short times, but will ultimately fail if the run time becomes too long. There is also a tradeoff between the length of time one can run a simulation out to and the time jitter of the stroboscopic measurements that must be balanced when planning to employ this mapping.

Universality from disorder in the random-bond Blume-Capel model

NASA Astrophysics Data System (ADS)

Fytas, N. G.; Zierenberg, J.; Theodorakis, P. E.; Weigel, M.; Janke, W.; Malakis, A.

2018-04-01

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L*≈32 for the chosen parameters.

Long-range Ising model for credit portfolios with heterogeneous credit exposures

NASA Astrophysics Data System (ADS)

Kato, Kensuke

2016-11-01

We propose the finite-size long-range Ising model as a model for heterogeneous credit portfolios held by a financial institution in the view of econophysics. The model expresses the heterogeneity of the default probability and the default correlation by dividing a credit portfolio into multiple sectors characterized by credit rating and industry. The model also expresses the heterogeneity of the credit exposure, which is difficult to evaluate analytically, by applying the replica exchange Monte Carlo method to numerically calculate the loss distribution. To analyze the characteristics of the loss distribution for credit portfolios with heterogeneous credit exposures, we apply this model to various credit portfolios and evaluate credit risk. As a result, we show that the tail of the loss distribution calculated by this model has characteristics that are different from the tail of the loss distribution of the standard models used in credit risk modeling. We also show that there is a possibility of different evaluations of credit risk according to the pattern of heterogeneity.

The theory of maximally and minimally even sets, the one- dimensional antiferromagnetic Ising model, and the continued fraction compromise of musical scales

NASA Astrophysics Data System (ADS)

Douthett, Elwood (Jack) Moser, Jr.

1999-10-01

Cyclic configurations of white and black sites, together with convex (concave) functions used to weight path length, are investigated. The weights of the white set and black set are the sums of the weights of the paths connecting the white sites and black sites, respectively, and the weight between sets is the sum of the weights of the paths that connect sites opposite in color. It is shown that when the weights of all configurations of a fixed number of white and a fixed number of black sites are compared, minimum (maximum) weight of a white set, minimum (maximum) weight of the a black set, and maximum (minimum) weight between sets occur simultaneously. Such configurations are called maximally even configurations. Similarly, the configurations whose weights are the opposite extremes occur simultaneously and are called minimally even configurations. Algorithms that generate these configurations are constructed and applied to the one- dimensional antiferromagnetic spin-1/2 Ising model. Next the goodness of continued fractions as applied to musical intervals (frequency ratios and their base 2 logarithms) is explored. It is shown that, for the intermediate convergents between two consecutive principal convergents of an irrational number, the first half of the intermediate convergents are poorer approximations than the preceding principal convergent while the second half are better approximations; the goodness of a middle intermediate convergent can only be determined by calculation. These convergents are used to determine what equal-tempered systems have intervals that most closely approximate the musical fifth (pn/ qn = log2(3/2)). The goodness of exponentiated convergents ( 2pn/qn~3/2 ) is also investigated. It is shown that, with the exception of a middle convergent, the goodness of the exponential form agrees with that of its logarithmic Counterpart As in the case of the logarithmic form, the goodness of a middle intermediate convergent in the exponential form can only be determined by calculation. A Desirability Function is constructed that simultaneously measures how well multiple intervals fit in a given equal-tempered system. These measurements are made for octave (base 2) and tritave systems (base 3). Combinatorial properties important to music modulation are considered. These considerations lead These considerations lead to the construction of maximally even scales as partitions of an equal-tempered system.

Formalization of the classification pattern: survey of classification modeling in information systems engineering.

PubMed

Partridge, Chris; de Cesare, Sergio; Mitchell, Andrew; Odell, James

2018-01-01

Formalization is becoming more common in all stages of the development of information systems, as a better understanding of its benefits emerges. Classification systems are ubiquitous, no more so than in domain modeling. The classification pattern that underlies these systems provides a good case study of the move toward formalization in part because it illustrates some of the barriers to formalization, including the formal complexity of the pattern and the ontological issues surrounding the "one and the many." Powersets are a way of characterizing the (complex) formal structure of the classification pattern, and their formalization has been extensively studied in mathematics since Cantor's work in the late nineteenth century. One can use this formalization to develop a useful benchmark. There are various communities within information systems engineering (ISE) that are gradually working toward a formalization of the classification pattern. However, for most of these communities, this work is incomplete, in that they have not yet arrived at a solution with the expressiveness of the powerset benchmark. This contrasts with the early smooth adoption of powerset by other information systems communities to, for example, formalize relations. One way of understanding the varying rates of adoption is recognizing that the different communities have different historical baggage. Many conceptual modeling communities emerged from work done on database design, and this creates hurdles to the adoption of the high level of expressiveness of powersets. Another relevant factor is that these communities also often feel, particularly in the case of domain modeling, a responsibility to explain the semantics of whatever formal structures they adopt. This paper aims to make sense of the formalization of the classification pattern in ISE and surveys its history through the literature, starting from the relevant theoretical works of the mathematical literature and gradually shifting focus to the ISE literature. The literature survey follows the evolution of ISE's understanding of how to formalize the classification pattern. The various proposals are assessed using the classical example of classification; the Linnaean taxonomy formalized using powersets as a benchmark for formal expressiveness. The broad conclusion of the survey is that (1) the ISE community is currently in the early stages of the process of understanding how to formalize the classification pattern, particularly in the requirements for expressiveness exemplified by powersets, and (2) that there is an opportunity to intervene and speed up the process of adoption by clarifying this expressiveness. Given the central place that the classification pattern has in domain modeling, this intervention has the potential to lead to significant improvements.

High-dimensional inference with the generalized Hopfield model: principal component analysis and corrections.

PubMed

Cocco, S; Monasson, R; Sessak, V

2011-05-01

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that maximum likelihood inference is deeply related to principal component analysis when the amplitude of the pattern components ξ is negligible compared to √N. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in ξ/√N. We stress the need to generalize the Hopfield model and include both attractive and repulsive patterns in order to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size N and of the amplitude ξ. The inference approach is illustrated on synthetic and biological data.

Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams

NASA Astrophysics Data System (ADS)

Chan, C. H.; Brown, G.; Rikvold, P. A.

2017-05-01

A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multivariable density of states is obtained for one set of values of fieldlike model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multivariable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The fieldlike parameters in this model are an effective magnetic field and the strength of the long-range interaction.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Ion sensing method

DOEpatents

Smith, Richard Harding; Martin, Glenn Brian

2004-05-18

The present invention allows the determination of trace levels of ionic substances in a sample solution (ions, metal ions, and other electrically charged molecules) by coupling a separation method, such as liquid chromatography, with ion selective electrodes (ISE) prepared so as to allow detection at activities below 10.sup.-6 M. The separation method distributes constituent molecules into fractions due to unique chemical and physical properties, such as charge, hydrophobicity, specific binding interactions, or movement in an electrical field. The separated fractions are detected by means of the ISE(s). These ISEs can be used singly or in an array. Accordingly, modifications in the ISEs are used to permit detection of low activities, specifically, below 10.sup.-6 M, by using low activities of the primary analyte (the molecular species which is specifically detected) in the inner filling solution of the ISE. Arrays constructed in various ways allow flow-through sensing for multiple ions.

Phase diagram of the frustrated J 1 ‑ J 2 transverse field Ising model on the square lattice

NASA Astrophysics Data System (ADS)

Sadrzadeh, M.; Langari, A.

2018-03-01

We study the zero-temperature phase diagram of transverse field Ising model on the J 1 ‑ J 2 square lattice. In zero magnetic field, the model has a classical Néel phase for J 2/J 1 < 0.5 and an antiferromagnetic collinear phase for J 2/J 1 > 0.5. We incorporate harmonic fluctuations by using linear spin wave theory (LSWT) with single spin flip excitations above a magnetic order background and obtain the phase diagram of the model in this approximation. We find that harmonic quantum fluctuations of LSWT fail to lift the large degeneracy at J 2/J 1 = 0.5 and exhibit some inconsistent regions on the phase diagram. However, we show that anharmonic fluctuations of cluster operator approach (COA) resolve the inconsistency of the LSWT, which reveals a string-valence bond solid ordered phase for the highly frustrated region.

Influence of sad mood induction on implicit self-esteem and its relationship with symptoms of depression and anxiety.

PubMed

van Tuijl, Lonneke A; Verwoerd, Johan R L; de Jong, Peter J

2018-02-13

Implicit self-esteem (ISE) refers to the valence of triggered associations when the self is activated. Despite theories, previous studies often fail to observe low ISE in depression and anxiety. It is feasible that sad mood is required to activate dysfunctional self-associations. The present study tested the following hypotheses: i) ISE is lower following a sad mood induction (SMI); ii) the relationship between ISE and level of depression/anxiety symptoms is relatively strong when ISE is measured during sad mood; iii) individuals with higher levels of depression/anxiety symptoms will show a relatively large decrease in ISE following a SMI. In this mixed-designed study, university students completed the self-esteem implicit association test (IAT) either at baseline (control condition; n = 46) or following a SMI (experimental condition; n = 49). To test the third hypothesis, a SMI and IAT were also given in the control condition. Both conditions completed self-report measures of explicit self-esteem (ESE), and symptoms of depression and anxiety. There was no support for the first two hypotheses, but some support that symptoms of anxiety correlated with larger decreases in ISE following a SMI which partly supported the third hypothesis. This disappeared when controlling for multiple testing. Results are limited to non-clinical participants. While ISE was robust against increases in sad mood, there was some tentative support that symptoms of anxiety were related to larger decreases in ISE following a SMI. Copyright © 2018. Published by Elsevier Ltd.

Thermal contact through a two-temperature kinetic Ising chain

NASA Astrophysics Data System (ADS)

Bauer, M.; Cornu, F.

2018-05-01

We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different temperatures and kinetic parameters on alternating sites. The inhomogeneity of the kinetic parameter is a novelty with respect to the model of Racz and Zia (1994 Phys. Rev. E 49 139), and we exhibit its influence upon the stationary non equilibrium values of the two-spin correlations at any distance. By mapping to the dynamics of spin domain walls and using free fermion techniques, we determine the scaled generating function for the cumulants of the exchanged heat amounts per unit of time in the long time limit.

The NASA Radiation Interuniversity Science and Engineering(RaISE) Project: A Model for Inter-collaboration and Distance Learning in Radiation Physics and Nuclear Engineering

NASA Technical Reports Server (NTRS)

Denkins, Pamela S.; Saganti, P.; Obot, V.; Singleterry, R.

2006-01-01

This viewgraph document reviews the Radiation Interuniversity Science and Engineering (RaISE) Project, which is a project that has as its goals strengthening and furthering the curriculum in radiation sciences at two Historically Black Colleges and Universities (HBCU), Prairie View A&M University and Texas Southern University. Those were chosen in part because of the proximity to NASA Johnson Space Center, a lead center for the Space Radiation Health Program. The presentation reviews the courses that have been developed, both in-class, and on-line.

The use of laboratory experiments for the study of conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Silliman, S. E.; Zheng, L.; Conwell, P.

Laboratory experiments on heterogeneous porous media (otherwise known as intermediate scale experiments, or ISEs) have been increasingly relied upon by hydrogeologists for the study of saturated and unsaturated groundwater systems. Among the many ongoing applications of ISEs is the study of fluid flow and the transport of conservative solutes in correlated permeability fields. Recent advances in ISE design have provided the capability of creating correlated permeability fields in the laboratory. This capability is important in the application of ISEs for the assessment of recent stochastic theories. In addition, pressure-transducer technology and visualization methods have provided the potential for ISEs to be used in characterizing the spatial distributions of both hydraulic head and local water velocity within correlated permeability fields. Finally, various methods are available for characterizing temporal variations in the spatial distribution (and, thereby, the spatial moments) of solute concentrations within ISEs. It is concluded, therefore, that recent developments in experimental techniques have provided an opportunity to use ISEs as important tools in the continuing study of fluid flow and the transport of conservative solutes in heterogeneous, saturated porous media. Résumé Les hydrogéologues se sont progressivement appuyés sur des expériences de laboratoire sur des milieux poreux hétérogènes (connus aussi par l'expression "Expériences àéchelle intermédiaire", ISE) pour étudier les zones saturées et non saturées des aquifères. Parmi les nombreuses applications en cours des ISE, il faut noter l'étude de l'écoulement de fluide et le transport de solutés conservatifs dans des champs aux perméabilités corrélées. Les récents progrès du protocole des ISE ont donné la possibilité de créer des champs de perméabilités corrélées au laboratoire. Cette possibilité est importante dans l'application des ISE pour l'évaluation des théories stochastiques récentes. En outre, la technologie des capteurs de pression et les méthodes de visualisation donnent la possibilité d'utiliser les ISE pour caractériser les distributions spatiales à la fois de la piézométrie et de la vitesse locale de l'eau dans un champs de perméabilités corrélées. Finalement, des méthodes variées peuvent être utilisées pour caractériser les variations temporelles de la distribution spatiale (et, par conséquent, les moments spatiaux) des concentrations de soluté dans les ISE. En conclusion, donc, des développements récents des techniques expérimentales ont fourni l'occasion d'utiliser les ISE comme d'importants outils d'étude en continu des écoulement de fluides et de transport de solutés conservatifs dans des milieux poreux saturés hétérogènes. Resumen Los experimentos de laboratorio en medio poroso heterogéneo (conocidos como Experimentos a Escala Intermedia o ISE) están cada vez mejor considerados para el estudio de los sistemas saturados y no saturados. Entre las muchas aplicaciones de los ISE se encuentra el estudio del flujo y el transporte de solutos conservativos en medios con permeabilidad que presentan una cierta estructura de correlación. Avances recientes en el diseño de los ISE han proporcionado la capacidad de crear medios de este tipo en el laboratorio. Esta capacidad es importante para la aplicación de los ISE a la evaluación de las teorías estocásticas recientes. Además, la tecnología de los transductores de presión y los métodos de visualización han permitido que los ISE se usen para caracterizar la distribución espacial de niveles hidráulicos y de las velocidades locales del agua en campos de permeabilidad con determinada correlación espacial. Finalmente, existen varios métodos para caracterizar las variaciones temporales en la distribución espacial (y por tanto los momentos estadísticos espaciales) de la concentración de solutos en los ISE. Se concluye que los desarrollos recientes en las técnicas experimentales han proporcionado una oportunidad para usar los ISE como herramientas fundamentales en el estudio del flujo y transporte de solutos conservativos en medio poroso heterogéneo y saturado.

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

Three-dimensional magnetosheath plasma ion distributions from 200 eV to 2 MeV

NASA Technical Reports Server (NTRS)

Williams, D. J.; Mitchell, D. G.; Frank, L. A.; Eastman, T. E.

1988-01-01

This paper presents initial measurements, made with ISEE 1 plasma and energetic-particle instruments, of the three-dimensional magnetosheath plasma ion flow and the spectrum over the energy range of 200 eV to 2 MeV, obtained on two magnetosheath traversals, one on the dawn (December 19, 1977) and the other on the dusk (July 7, 1978) flanks of the magnetosphere. The data suggest that the magnetosheath plasma ion population often consisted of a shocked solar wind component, of energy not greater than 5 keV, and a magnetospheric high-energy (not below 5 keV) component. The shocked solar wind component generally behaved independently of the magnetic field direction, indicating that the magnetic field was carried along in the bulk plasma flow. The high-energy tail was highly modulated by the magnetic field.

Exactly solved mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lisnyi, Bohdan; Strečka, Jozef

2015-03-01

The mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration-iteration transformation and the transfer-matrix method. The decoration-iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively.

Ground-state and magnetocaloric properties of a coupled spin-electron double-tetrahedral chain (exact study at the half filling)

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Jakubczyk, Dorota

2017-01-01

Ground-state and magnetocaloric properties of a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters half filled with mobile electrons, are exactly investigated by using the transfer-matrix method in combination with the construction of the Nth tensor power of the discrete Fourier transformation. It is shown that the ground state of the model is formed by two non-chiral phases with the zero residual entropy and two chiral phases with the finite residual entropy S = NkB ln 2. Depending on the character of the exchange interaction between the localized Ising spins and mobile electrons, one or three magnetization plateaus can be observed in the magnetization process. Their heights basically depend on the values of Landé g-factors of the Ising spins and mobile electrons. It is also evidenced that the system exhibits both the conventional and inverse magnetocaloric effect depending on values of the applied magnetic field and temperature.

Validation of a Real-Time ISE Methodology to Quantify the Influence of Inhibitors of Demineralization Kinetics in vitro Using a Hydroxyapatite Model System.

PubMed

Huang, Wei-Te; Shahid, Saroash; Anderson, Paul

2018-05-25

The aim was to validate a novel protocol to measure the cariostatic efficacies of demineralization inhibitors by repeating previous SMR (scanning microradiography) studies investigating the dose response of Zn2+ and F- on demineralization kinetics in vitro using real-time Ca2+ ion selective electrodes (ISEs). In this study, Ca2+ release was used as a proxy for the extent of demineralization. Forty-eight hydroxyapatite (HAP) discs were allocated into 16 groups (n = 3) and adding either increasing [Zn2+], or [F-], similar to those used in the previous SMR studies. Each HAP disc was immersed in 50 mL, pH 4.0, buffered acetic acid for 1 h, and real-time ISE methodology was used to monitor the rate of increase in [Ca2+] in the demineralization solution. Next, either zinc acetate or sodium fluoride was added into each demineralization solution accordingly. Then after each [Zn2+] or [F-] addition, the HAP disc was further demineralized for 1 h, and ISE measurements were continued. The percentage reduction in the rate of calcium loss from hydroxyapatite (PRCLHAP) at each [Zn2+] or [F-] was calculated from the decrease in Ca2+ release rate, similar to that used in the previous SMR studies. A log-linear relationship between mean PRCLHAP and inhibitor concentration was found for both Zn2+ and F-, similar to that reported for each ion in the previous SMR studies. In conclusion, real-time Ca2+ ISE systems can be used to measure the cariostatic efficacies of demineralization inhibitors. © 2018 S. Karger AG, Basel.

Immortalization-susceptible elements and their binding factors mediate rejuvenation of regulation of the type I collagenase gene in simian virus 40 large T antigen-transformed immortal human fibroblasts.

PubMed Central

Imai, S; Fujino, T; Nishibayashi, S; Manabe, T; Takano, T

1994-01-01

Dramatic changes occur in expression of the type I collagenase gene during the process of immortalization in simian virus 40 large T antigen-transformed human fibroblasts (S. Imai and T. Takano, Biochem. Biophys. Res. Commun. 189:148-153, 1992). From transient transfection assays, it was determined that these changes involved the functions of two immortalization-susceptible cis-acting elements, ISE1 and ISE2, located in a 100-bp region about 1.7 kb upstream. The profiles of binding of an activator, Proserpine, to the enhancer ISE1 were similar in the extracts of young, senescent preimmortalized and immortalized cells. ISE2 contained both negative and positive regulatory elements located adjacent to each other. The positive regulatory element consisted of a tandem array of putative Ets family- and AP-1-binding sites. An activator, Pluto, interacted with this positive regulatory element and had an AP-1-related component as a complex. The binding activity of Pluto was predominantly detected only in the extract from senescent preimmortalized cells. In contrast, a repressor, Orpheus, which bound to the ATG-rich negative regulatory element of ISE2, was prominently detected in extracts from both young preimmortalized and immortalized cells and appeared to suppress transcription in an orientation-dependent manner. Thus, the interplay of Pluto and Orpheus was suggested to be crucial for regulation of the collagenase gene accompanying in vitro aging and immortalization. Proserpine seemed to interact with Pluto to mediate strong expression of the collagenase gene in cellular senescence. On the basis of these results, we propose a model for regulation of the collagenase gene during in vitro aging and immortalization. Images PMID:7935433

The Subsurface Flow and Transport Laboratory: A New Department of Energy User's Facility for Intermediate-Scale Experimentation

NASA Astrophysics Data System (ADS)

Wietsma, T. W.; Oostrom, M.; Foster, N. S.

2003-12-01

Intermediate-scale experiments (ISEs) for flow and transport are a valuable tool for simulating subsurface features and conditions encountered in the field at government and private sites. ISEs offer the ability to study, under controlled laboratory conditions, complicated processes characteristic of mixed wastes and heterogeneous subsurface environments, in multiple dimensions and at different scales. ISEs may, therefore, result in major cost savings if employed prior to field studies. A distinct advantage of ISEs is that researchers can design physical and/or chemical heterogeneities in the porous media matrix that better approximate natural field conditions and therefore address research questions that contain the additional complexity of processes often encountered in the natural environment. A new Subsurface Flow and Transport Laboratory (SFTL) has been developed for ISE users in the Environmental Spectroscopy & Biogeochemistry Facility in the Environmental Molecular Sciences Laboratory (EMSL) at Pacific Northwest National Laboratory (PNNL). The SFTL offers a variety of columns and flow cells, a new state-of-the-art dual-energy gamma system, a fully automated saturation-pressure apparatus, and analytical equipment for sample processing. The new facility, including qualified staff, is available for scientists interested in collaboration on conducting high-quality flow and transport experiments, including contaminant remediation. Close linkages exist between the SFTL and numerical modelers to aid in experimental design and interpretation. This presentation will discuss the facility and outline the procedures required to submit a proposal to use this unique facility for research purposes. The W. R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility, is sponsored by the U.S. Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory.

Randomly diluted xy and resistor networks near the percolation threshold

NASA Astrophysics Data System (ADS)

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

1987-05-01

A formulation based on that of Stephen for randomly diluted systems near the percolation threshold is analyzed in detail. By careful consideration of various limiting procedures, a treatment of xy spin models and resistor networks is given which shows that previous calculations (which indicate that these systems having continuous symmetry have the same crossover exponents as the Ising model) are in error. By studying the limit wherein the energy gap goes to zero, we exhibit the mathematical mechanism which leads to qualitatively different results for xy-like as contrasted to Ising-like systems. A distinctive feature of the results is that there is an infinite sequence of crossover exponents needed to completely describe the probability distribution for R(x,x'), the resistance between sites x and x'. Because of the difference in symmetry between the xy model and the resistor network, the former has an infinite sequence of crossover exponents in addition to those of the resistor network. The first crossover exponent φ1=1+ɛ/42 governs the scaling behavior of R(x,x') with ||x-x'||≡r: [R(x,x')]c~xφ1/ν, where [ ]c indicates a conditional average, subject to x and x' being in the same cluster, ν is the correlation length exponent for percolation, and ɛ=6-d, where d is the spatial dimensionality. We give a detailed analysis of the scaling properties of the bulk conductivity and the anomalous diffusion constant introduced by Gefen et al. Our results show conclusively that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, at least in high spatial dimension. We also evaluate various amplitude ratios associated with susceptibilities, χn involving the nth power of the resistance R(x,x'), e.g., &χ2χ0/χ21=2[1+(19ɛ/420)]. In an appendix we outline how the calculation can be extended to treat the diluted m-component spin model for m>2. As expected, the results for φ1 remain valid for m>2. The techniques described here have led to several recent calculations of various infinite families of exponents.

Ferromagnetic transition in a simple variant of the Ising model on multiplex networks

NASA Astrophysics Data System (ADS)

Krawiecki, A.

2018-02-01

Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, a simple variant of the Ising model on multiplex networks with two layers is considered, with spins located in the nodes and edges corresponding to ferromagnetic interactions between them. Critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random Erdös-Rényi graphs or heterogeneous scale-free networks using the mean-field approximation and the replica method, from the replica symmetric solution. Both methods require the use of different "partial" magnetizations, associated with different layers of the multiplex network, and yield qualitatively similar results. If the layers are strongly heterogeneous the critical temperature differs noticeably from that for the Ising model on a network being a superposition of the two layers, evaluated in the mean-field approximation neglecting the effect of the underlying multiplex structure on the correlations between the degrees of nodes. The critical temperature evaluated from the replica symmetric solution depends sensitively on the correlations between the degrees of nodes in different layers and shows satisfactory quantitative agreement with that obtained from Monte Carlo simulations. The critical behavior of the magnetization for the model with strongly heterogeneous layers can depend on the distributions of the degrees of nodes and is then determined by the properties of the most heterogeneous layer.

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 ).

A Statewide Partnership for Implementing Inquiry Science

NASA Astrophysics Data System (ADS)

Lytle, Charles

The North Carolina Infrastructure for Science Education (NC-ISE) is a statewide partnership for implementing standards-based inquiry science using exemplary curriculum materials in the public schools of North Carolina. North Carolina is the 11th most populous state in the USA with 8,000,000 residents, 117 school districts and a geographic area of 48,718 miles. NC-ISE partners include the state education agency, local school systems, three branches of the University of North Carolina, the state mathematics and science education network, businesses, and business groups. The partnership, based upon the Science for All Children model developed by the National Science Resources Centre, was initiated in 1997 for improvement in teaching and learning of science and mathematics. This research-based model has been successfully implemented in several American states during the past decade. Where effectively implemented, the model has led to significant improvements in student interest and student learning. It has also helped reduce the achievement gap between minority and non-minority students and among students from different economic levels. A key program element of the program is an annual Leadership Institute that helps teams of administrators and teachers develop a five-year strategic plan for their local systems. Currently 33 of the117 local school systems have joined the NC-ISE Program and are in various stages of implementation of inquiry science in grades K-8.

Localization and Symmetry Breaking in the Quantum Quasiperiodic Ising Glass

NASA Astrophysics Data System (ADS)

Chandran, A.; Laumann, C. R.

2017-07-01

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable long-range orders forbidden in equilibrium. Specifically, we show that the interplay of symmetry breaking and localization in the quasiperiodic quantum Ising chain produces a quasiperiodic Ising glass stable at all energy densities. The glass order parameter vanishes with an essential singularity at the melting transition with no signatures in the equilibrium properties. The zero-temperature phase diagram is also surprisingly rich, consisting of paramagnetic, ferromagnetic, and quasiperiodically alternating ground-state phases with extended, localized, and critically delocalized low-energy excitations. The system exhibits an unusual quantum Ising transition whose properties are intermediate between those of the clean and infinite randomness Ising transitions. Many of these results follow from a geometric generalization of the Aubry-André duality that we develop. The quasiperiodic Ising glass may be realized in near-term quantum optical experiments.

Nuclear and ionic charge distribution experiment on ISEE-1 and ISEE-3

NASA Technical Reports Server (NTRS)

Gloeckler, G.; Ipavich, F. M.; Galvin, A. B.

1987-01-01

The experimental work carried out under this contract is a continuation of that originally performed under Contracts NAS5-20062 and NAS5-26739. The data analyzed are from the Max-Planck Institut/Univ. of Maryland experiment on ISEE-1 and ISEE-3. Each spacecraft experiment consists of a nearly identical set of three sensors (designated the ULECA, ULEWAT, and ULEZEQ sensors) designed to measure the energy spectra and composition of suprathermal and energetic ions over a broad energy range (less than 3 keV/e to more than 20 MeV/nucleon). Since the launch of ISEE's 2 and 3, the MPI/Univ. of Maryland experiments have generally performed as expected except for a partial failure of the ULEWAT sensor on ISEE-1 in August 1978. A number of scientific studies have either been completed, initiated or are at various stages of completion. A brief summary of Primary Results is given, followed by a more detailed summary of the major accomplishments at the Univ. of Maryland.

On the use of a sunward-libration-point orbiting spacecraft as an IMF monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1984-01-01

Magnetospheric studies often require knowledge of the orientation of the IMF. In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point for this purpose, the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting Earth, has been calculated for a data set of two-hour periods covering four months. For each period, a ten-minute average of ISEE 1 data is compared with ten-minute averages of ISEE 3 data at successively lagged intervals. At the lag time equal to the time required for the solar wind to convect from ISEE 3 to ISEE 1, the median angle between the IMF orientation at the two spacecraft is 20 deg, and 80% of the cases have angles less than 38 deg. The results for the angles projected on the y-z plane are essentially the same.

Some Aspects of Mathematical Model of Collaborative Learning

ERIC Educational Resources Information Center

Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

2012-01-01

There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

Ion Fluxes in Giant Excised Cardiac Membrane Patches Detected and Quantified with Ion-selective Microelectrodes

PubMed Central

Kang, Tong Mook; Markin, Vladislav S.; Hilgemann, Donald W.

2003-01-01

We have used ion-selective electrodes (ISEs) to quantify ion fluxes across giant membrane patches by measuring and simulating ion gradients on both membrane sides. Experimental conditions are selected with low concentrations of the ions detected on the membrane side being monitored. For detection from the cytoplasmic (bath) side, the patch pipette is oscillated laterally in front of an ISE. For detection on the extracellular (pipette) side, ISEs are fabricated from flexible quartz capillary tubing (tip diameters, 2–3 microns), and an ISE is positioned carefully within the patch pipette with the tip at a controlled distance from the mouth of the patch pipette. Transport activity is then manipulated by solution changes on the cytoplasmic side. Ion fluxes can be quantified by simulating the ion gradients with appropriate diffusion models. For extracellular (intrapatch pipette) recordings, ion diffusion coefficients can be determined from the time courses of concentration changes. The sensitivity and utility of the methods are demonstrated with cardiac membrane patches by measuring (a) potassium fluxes via ion channels, valinomycin, and Na/K pumps; (b) calcium fluxes mediated by Na/Ca exchangers; (c) sodium fluxes mediated by gramicidin and Na/K pumps; and (d) proton fluxes mediated by an unknown electrogenic mechanism. The potassium flux-to-current ratio for the Na/K pump is approximately twice that determined for potassium channels and valinomycin, as expected for a 3Na/2K pump stoichiometery (i.e., 2K/charge moved). For valinomycin-mediated potassium currents and gramicidin-mediated sodium currents, the ion fluxes calculated from diffusion models are typically 10–15% smaller than expected from the membrane currents. As presently implemented, the ISE methods allow reliable detection of calcium and proton fluxes equivalent to monovalent cation currents <1 pA in magnitude, and they allow detection of sodium and potassium fluxes equivalent to <5 pA currents. The capability to monitor ion fluxes, independent of membrane currents, should facilitate studies of both electrogenic and electroneutral ion–coupled transporters in giant patches. PMID:12668735

Domain-wall excitations in the two-dimensional Ising spin glass

NASA Astrophysics Data System (ADS)

Khoshbakht, Hamid; Weigel, Martin

2018-02-01

The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to 10 000 ×10 000 spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic case. Based on these techniques, a large number of disorder samples are used together with a careful finite-size scaling analysis to determine the stiffness exponents and domain-wall fractal dimensions with unprecedented accuracy, our best estimates being θ =-0.2793 (3 ) and df=1.273 19 (9 ) for Gaussian couplings. For bimodal disorder, a new uniform sampling algorithm allows us to study the domain-wall fractal dimension, finding df=1.279 (2 ) . Additionally, we also investigate the distributions of ground-state energies, of domain-wall energies, and domain-wall lengths.

In Situ Monitoring of Pb2+ Leaching from the Galvanic Joint Surface in a Prepared Chlorinated Drinking Water.

PubMed

Ma, Xiangmeng; Armas, Stephanie M; Soliman, Mikhael; Lytle, Darren A; Chumbimuni-Torres, Karin; Tetard, Laurene; Lee, Woo Hyoung

2018-02-20

A novel method using a micro-ion-selective electrode (micro-ISE) technique was developed for in situ lead monitoring at the water-metal interface of a brass-leaded solder galvanic joint in a prepared chlorinated drinking water environment. The developed lead micro-ISE (100 μm tip diameter) showed excellent performance toward soluble lead (Pb 2+ ) with sensitivity of 22.2 ± 0.5 mV decade -1 and limit of detection (LOD) of 1.22 × 10 -6 M (0.25 mg L -1 ). The response time was less than 10 s with a working pH range of 2.0-7.0. Using the lead micro-ISE, lead concentration microprofiles were measured from the bulk to the metal surface (within 50 μm) over time. Combined with two-dimensional (2D) pH mapping, this work clearly demonstrated that Pb 2+ ions build-up across the lead anode surface was substantial, nonuniform, and dependent on local surface pH. A large pH gradient (ΔpH = 6.0) developed across the brass and leaded-tin solder joint coupon. Local pH decreases were observed above the leaded solder to a pH as low as 4.0, indicating it was anodic relative to the brass. The low pH above the leaded solder supported elevated lead levels where even small local pH differences of 0.6 units (ΔpH = 0.6) resulted in about four times higher surface lead concentrations (42.9 vs 11.6 mg L -1 ) and 5 times higher fluxes (18.5 × 10 -6 vs 3.5 × 10 -6 mg cm -2 s -1 ). Continuous surface lead leaching monitoring was also conducted for 16 h.

ISEES: an institute for sustainable software to accelerate environmental science

NASA Astrophysics Data System (ADS)

Jones, M. B.; Schildhauer, M.; Fox, P. A.

2013-12-01

Software is essential to the full science lifecycle, spanning data acquisition, processing, quality assessment, data integration, analysis, modeling, and visualization. Software runs our meteorological sensor systems, our data loggers, and our ocean gliders. Every aspect of science is impacted by, and improved by, software. Scientific advances ranging from modeling climate change to the sequencing of the human genome have been rendered possible in the last few decades due to the massive improvements in the capabilities of computers to process data through software. This pivotal role of software in science is broadly acknowledged, while simultaneously being systematically undervalued through minimal investments in maintenance and innovation. As a community, we need to embrace the creation, use, and maintenance of software within science, and address problems such as code complexity, openness,reproducibility, and accessibility. We also need to fully develop new skills and practices in software engineering as a core competency in our earth science disciplines, starting with undergraduate and graduate education and extending into university and agency professional positions. The Institute for Sustainable Earth and Environmental Software (ISEES) is being envisioned as a community-driven activity that can facilitate and galvanize activites around scientific software in an analogous way to synthesis centers such as NCEAS and NESCent that have stimulated massive advances in ecology and evolution. We will describe the results of six workshops (Science Drivers, Software Lifecycles, Software Components, Workforce Development and Training, Sustainability and Governance, and Community Engagement) that have been held in 2013 to envision such an institute. We will present community recommendations from these workshops and our strategic vision for how ISEES will address the technical issues in the software lifecycle, sustainability of the whole software ecosystem, and the critical issue of computational training for the scientific community. Process for envisioning ISEES.

Solar wind-magnetosphere coupling and the distant magnetotail: ISEE-3 observations

NASA Technical Reports Server (NTRS)

Slavin, J. A.; Smith, E. J.; Sibeck, D. G.; Baker, D. N.; Zwickl, R. D.; Akasofu, S. I.; Lepping, R. P.

1985-01-01

ISEE-3 Geotail observations are used to investigate the relationship between the interplanetary magnetic field, substorm activity, and the distant magnetotail. Magnetic field and plasma observations are used to present evidence for the existence of a quasi-permanent, curved reconnection neutral line in the distant tail. The distance to the neutral line varies from absolute value of X = 120 to 140 R/sub e near the center of the tail to beyond absolute value of X = 200 R/sub e at the flanks. Downstream of the neutral line the plasma sheet magnetic field is shown to be negative and directly proportional to negative B/sub z in the solar wind as observed by IMP-8. V/sub x in the distant plasma sheet is also found to be proportional to IMF B/sub z with southward IMF producing the highest anti-solar flow velocities. A global dayside reconnection efficiency of 20 +- 5% is derived from the ISEE-3/IMP-8 magnetic field comparisons. Substorm activity, as measured by the AL index, produces enhanced negative B/sub z and tailward V/sub x in the distant plasma sheet in agreement with the basic predictions of the reconnection-based models of substorms. The rate of magnetic flux transfer out of the tail as a function of AL is found to be consistent with previous near-Earth studies. Similarly, the mass and energy fluxes carried by plasma sheet flow down the tail are consistent with theoretical mass and energy budgets for an open magnetosphere. In summary, the ISEE-3 Geotail observations appear to provide good support for reconnection models of solar wind-magnetosphere coupling and substorm energy rates.

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.

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

The acceleration of charged particles in interplanetary shock waves

NASA Technical Reports Server (NTRS)

Pesses, M. E.; Decker, R. B.; Armstrong, T. P.

1982-01-01

Consideration of the theoretical and observational literature on energetic ion acceleration in interplanetary shock waves is the basis for the present discussion of the shock acceleration of the solar wind plasma and particle transport effects. It is suggested that ISEE data be used to construct data sets for shock events that extend continuously from solar wind to galactic cosmic ray energies, including data for electrons, protons, alphas and ions with Z values greater than 2.0, and that the temporal and spatial evolution of two- and three-dimensional particle distribution functions be studied by means of two or more spacecraft.

Fluxoids behavior in superconducting ladders

NASA Astrophysics Data System (ADS)

Sharon, Omri J.; Haham, Noam; Shaulov, Avner; Yeshurun, Yosef

2018-03-01

The nature of the interaction between fluxoids and between them and the external magnetic field is studied in one-dimensional superconducting networks. An Ising like expression is derived for the energy of a network revealing that fluxoids behave as repulsively interacting objects driven towards the network center by the effective applied field. Competition between these two interactions determines the equilibrium arrangement of fluxoids in the network as a function of the applied field. It is demonstrated that the fluxoids configurations are not always commensurate to the network symmetry. Incommensurate, degenerated configurations may be formed even in networks with an odd number of loops.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model

NASA Astrophysics Data System (ADS)

O'Brien, Edward; Fendley, Paul

2018-05-01

We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.

Robust criticality of an Ising model on rewired directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Gontarek, Krzysztof; Lipowska, Dorota

2015-06-01

We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.