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Sample records for dimensional ising model

  1. One-Dimensional Ising Model with "k"-Spin Interactions

    ERIC Educational Resources Information Center

    Fan, Yale

    2011-01-01

    We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

  2. Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space.

    PubMed

    Nakayama, Yu

    2016-04-01

    Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries.

  3. One-dimensional Ising model with multispin interactions

    NASA Astrophysics Data System (ADS)

    Turban, Loïc

    2016-09-01

    We study the spin-1/2 Ising chain with multispin interactions K involving the product of m successive spins, for general values of m. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions and we calculate the two-spin correlation function. When placed in an external field H the system is shown to be self-dual. Using another change of spin variables the one-dimensional Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions K and H. The 2D system, with size m × N/m, has the topology of a cylinder with helical BC. In the thermodynamic limit N/m\\to ∞ , m\\to ∞ , a 2D critical singularity develops on the self-duality line, \\sinh 2K\\sinh 2H=1.

  4. n-vicinities method for three dimensional Ising Model

    NASA Astrophysics Data System (ADS)

    Kryzhanovsky, Boris; Litinskii, Leonid

    2016-08-01

    The n -vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to the Ising model on the D - dimensional cubic lattice. The state equation is solved for an arbitrary dimension D and the behavior of the free energy is analyzed. For large values of D (D > 2) the obtained results are in good agreement with the ones obtained by means of computer simulations. For small values of D, there are noticeable discrepancies with the exact results.

  5. Linear relaxation in large two-dimensional Ising models

    NASA Astrophysics Data System (ADS)

    Lin, Y.; Wang, F.

    2016-02-01

    Critical dynamics in two-dimension Ising lattices up to 2048 ×2048 is simulated on field-programmable-gate-array- based computing devices. Linear relaxation times are measured from extremely long Monte Carlo simulations. The longest simulation has 7.1 ×1016 spin updates, which would take over 37 years to simulate on a general purpose computer. The linear relaxation time of the Ising lattices is found to follow the dynamic scaling law for correlation lengths as long as 2048. The dynamic exponent z of the system is found to be 2.179(12), which is consistent with previous studies of Ising lattices with shorter correlation lengths. It is also found that Monte Carlo simulations of critical dynamics in Ising lattices larger than 512 ×512 are very sensitive to the statistical correlations between pseudorandom numbers, making it even more difficult to study such large systems.

  6. One-dimensional random field Ising model and discrete stochastic mappings

    SciTech Connect

    Behn, U.; Zagrebnov, V.A.

    1987-06-01

    Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.

  7. Test of crossover scaling in the two-dimensional random-field Ising model

    NASA Astrophysics Data System (ADS)

    Binder, K.

    1984-05-01

    The random-field-induced rounding of the specific-heat singularity observed in transfer-matrix calculations of two-dimensional Ising models by Morgenstern, Binder, and Hornreich is interpreted in terms of the Fishman-Aharony scaling theory. Results qualitatively similar to recent experimental work on Rb2Co0.85Mg0.15F4 are obtained.

  8. Single-file water as a one-dimensional Ising model.

    PubMed

    Köfinger, Jürgen; Dellago, Christoph

    2010-09-27

    We show that single-file water in nanopores can be viewed as a one-dimensional Ising model and investigate, on this basis, the static dielectric response of a chain of hydrogen-bonded water molecules to an external field. To this end, we use a recently developed dipole lattice model which accurately captures the free energetics of nanopore water. In this model, the total energy of the system can be expressed as a sum of effective interactions of chain ends and orientational defects. Neglecting these interactions, we essentially obtain the one-dimensional Ising model which allows us to derive analytical expressions for the free energy as a function of the total dipole moment and for the dielectric susceptibility. Our expressions, which agree very well with simulation results, provide the basis for the interpretation of future dielectric spectroscopy experiments on water-filled nanopore membranes.

  9. Correlation functions in the two-dimensional Ising model in a magnetic field at T = Tc

    NASA Astrophysics Data System (ADS)

    Delfino, G.; Simonetti, P.

    1996-02-01

    The one- and two-particle form factors of the energy operator in the two-dimensional Ising model in a magnetic field at T = Tc are exactly computed within the form factor bootstrap approach. Together with the matrix elements of the magnetisation operator already computed by G. Delfino and G. Mussardo [Nucl. Phys. B 455 (1995) 724], they are used to write down the large distance expansion for the correlators of the two relevant fields of the model.

  10. The Finite-Size Scaling Relation for the Order-Parameter Probability Distribution of the Six-Dimensional Ising Model

    NASA Astrophysics Data System (ADS)

    Merdan, Ziya; Karakuş, Özlem

    2016-07-01

    The six dimensional Ising model with nearest-neighbor pair interactions has been simulated and verified numerically on the Creutz Cellular Automaton by using five bit demons near the infinite-lattice critical temperature with the linear dimensions L=4,6,8,10. The order parameter probability distribution for six dimensional Ising model has been calculated at the critical temperature. The constants of the analytical function have been estimated by fitting to probability function obtained numerically at the finite size critical point.

  11. Scaling and universality in the two-dimensional Ising model with a magnetic field

    NASA Astrophysics Data System (ADS)

    Mangazeev, Vladimir V.; Dudalev, Michael Yu.; Bazhanov, Vladimir V.; Batchelor, Murray T.

    2010-06-01

    The scaling function of the two-dimensional Ising model on the square and triangular lattices is obtained numerically via Baxter’s variational corner transfer-matrix approach. The use of Aharony-Fisher nonlinear scaling variables allowed us to perform calculations sufficiently away from the critical point and to confirm all predictions of the scaling and universality hypotheses. Our results are in excellent agreement with quantum field theory calculations of Fonseca and Zamolodchikov as well as with many previously known exact and numerical calculations, including susceptibility results by Barouch, McCoy, Tracy, and Wu.

  12. Flocking with discrete symmetry: The two-dimensional active Ising model

    NASA Astrophysics Data System (ADS)

    Solon, A. P.; Tailleur, J.

    2015-10-01

    We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.

  13. Critical behavior of the two-dimensional Ising model with long-range correlated disorder

    NASA Astrophysics Data System (ADS)

    Dudka, M.; Fedorenko, A. A.; Blavatska, V.; Holovatch, Yu.

    2016-06-01

    We study critical behavior of the diluted two-dimensional Ising model in the presence of disorder correlations which decay algebraically with distance as ˜r-a . Mapping the problem onto two-dimensional Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a nontrivial fixed point which is stable for 0.995

  14. Efficient Algorithms for the Two-Dimensional Ising Model with a Surface Field

    NASA Astrophysics Data System (ADS)

    Wu, Xintian

    2014-12-01

    The bond propagation and site propagation algorithms are extended to the two-dimensional (2D) Ising model with a surface field. With these algorithms we can calculate the free energy, internal energy, specific heat, magnetization, correlation functions, surface magnetization, surface susceptibility and surface correlations. The method can handle continuous and discrete bond and surface-field disorder and is especially efficient in the case of bond or site dilution. To test these algorithms, we study the wetting transition of the 2D Ising model, which was solved exactly by Abraham. We can locate the transition point accurately with a relative error of . We carry out the calculation of the specific heat and surface susceptibility on lattices with sizes up to . The results show that a finite jump develops in the specific heat and surface susceptibility at the transition point as the lattice size increases. For lattice size the parallel correlation length exponent is , while Abraham's exact result is . The perpendicular correlation length exponent for lattice size is , whereas its exact value is.

  15. A new look on the two-dimensional Ising model: thermal artificial spins

    NASA Astrophysics Data System (ADS)

    Arnalds, Unnar B.; Chico, Jonathan; Stopfel, Henry; Kapaklis, Vassilios; Bärenbold, Oliver; Verschuuren, Marc A.; Wolff, Ulrike; Neu, Volker; Bergman, Anders; Hjörvarsson, Björgvin

    2016-02-01

    We present a direct experimental investigation of the thermal ordering in an artificial analogue of an asymmetric two-dimensional Ising system composed of a rectangular array of nano-fabricated magnetostatically interacting islands. During fabrication and below a critical thickness of the magnetic material the islands are thermally fluctuating and thus the system is able to explore its phase space. Above the critical thickness the islands freeze-in resulting in an arrested thermalized state for the array. Determining the magnetic state we demonstrate a genuine artificial two-dimensional Ising system which can be analyzed in the context of nearest neighbor interactions.

  16. Critical two-dimensional Ising model with free, fixed ferromagnetic, fixed antiferromagnetic, and double antiferromagnetic boundaries.

    PubMed

    Wu, Xintian; Izmailyan, Nickolay

    2015-01-01

    The critical two-dimensional Ising model is studied with four types boundary conditions: free, fixed ferromagnetic, fixed antiferromagnetic, and fixed double antiferromagnetic. Using bond propagation algorithms with surface fields, we obtain the free energy, internal energy, and specific heat numerically on square lattices with a square shape and various combinations of the four types of boundary conditions. The calculations are carried out on the square lattices with size N×N and 30

  17. On the two-dimensional dynamical Ising model in the phase coexistence region

    NASA Astrophysics Data System (ADS)

    Martinelli, F.

    1994-09-01

    We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of side L, in the absence of an external field and at large inverse temperature β. We first consider the gap in the spectrum of the generator of the dynamics in two different cases: with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of -(1/β L) log(gap) as L→∞ and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase. Our results establish a connection between the dynamical large deviations and those of the equilibrium Gibbs measure studied by Shlosman in the framework of the rigorous description of the Wulff shape for the Ising model. Finally we show that, in the case of open boundary conditions, it is possible to rescale the time with L in such a way that, as L→∞, the finite-dimensional distributions of the time-rescaled magnetization converge to those of a symmetric continuous-time Markov chain on the two-state space {- m *(β), m *(β)}, m *(β) being the spontaneous magnetization. Our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric Markov chains on complicated graphs, developed by Jerrum and Sinclair in their Markov chain approach to hard computational problems, and the idea of introducing "block Glauber dynamics" instead of the standard single-site dynamics, in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium.

  18. CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES: Reduced Fidelity Susceptibility in One-Dimensional Transverse Field Ising Model

    NASA Astrophysics Data System (ADS)

    Ma, Jian; Xu, Lei; Wang, Xiao-Guang

    2010-01-01

    We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the one-dimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of logarithm, in contrast with the global ground-state fidelity susceptibility which is power divergence. In order to perform a scaling analysis, we take the square root of the susceptibility and determine the scaling exponent analytically and the result is further confirmed by numerical calculations.

  19. Phase Transition of Two-Dimensional Ising Models on the Honeycomb and Related Lattices with Striped Random Impurities

    NASA Astrophysics Data System (ADS)

    Morita, Satoshi; Suzuki, Sei

    2016-01-01

    Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings have the same magnitude, exact critical values for the fraction p of ferromagnetic bonds at the zero-temperature (T=0) are obtained. The critical lines in the p-T plane are drawn by numerically evaluating the Lyapunov exponent of random matrix products.

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

    PubMed

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

    2016-06-30

    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.

  1. 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.

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

    PubMed

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

    2016-06-30

    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. PMID:27281203

  3. Learning planar ising models

    SciTech Connect

    Johnson, Jason K; Chertkov, Michael; Netrapalli, Praneeth

    2010-11-12

    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 our attention on the class of planar Ising models, for which inference is tractable using techniques of statistical physics [Kac and Ward; Kasteleyn]. Based on these techniques and recent methods for planarity testing and planar embedding [Chrobak and Payne], we propose a simple greedy algorithm for learning the best 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. We present the results of numerical experiments evaluating the performance of our algorithm.

  4. Universality of the glassy transitions in the two-dimensional ±J Ising model.

    PubMed

    Parisen Toldin, Francesco; Pelissetto, Andrea; Vicari, Ettore

    2010-08-01

    We investigate the zero-temperature glassy transitions in the square-lattice ±J Ising model, with bond distribution P(J{xy})=pδ(J{xy}-J)+(1-p)δ(J{xy}+J) ; p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5 , which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p≈0.89 , and at p=1/2 . Their comparison provides a strong evidence that the glassy critical behavior that occurs for 1-p{0}

  5. Monte Carlo study of the two-dimensional site-diluted dipolar Ising model

    NASA Astrophysics Data System (ADS)

    Alonso, Juan J.; Allés, B.

    2010-08-01

    By tempered Monte Carlo simulations, we study two-dimensional site-diluted dipolar Ising systems. Dipoles are randomly placed on a fraction x of all L2 sites in a square lattice and point along a common crystalline axis. For xc0 range. Our results enable us to obtain an estimate of the critical exponent associated to the correlation length at T=0 , 1/ν=0.35(10) .

  6. Exploring the renormalization of quantum discord and Bell non-locality in the one-dimensional transverse Ising model

    NASA Astrophysics Data System (ADS)

    Liu, Cheng-cheng; Shi, Jia-dong; Ding, Zhi-yong; Ye, Liu

    2016-08-01

    In this paper, the effect of external magnet field g on the relationship among the quantum discord, Bell non-locality and quantum phase transition by employing quantum renormalization-group (QRG) method in the one-dimensional transverse Ising model is investigated. In our model, external magnet field g can influence the phase diagrams. The results have shown that both the two quantum correlation measures can develop two saturated values, which are associated with two distinct phases: long-ranged ordered Ising phase and the paramagnetic phase with the number of QRG iterations increasing. Additionally, quantum non-locality always existent in the long-ranged ordered Ising phase no matter whatever the value of g is and what times QRG steps are carried out and we conclude that the quantum non-locality always exists not only suitable for the two sites of block, but for nearest-neighbor blocks in the long-ranged ordered Ising phase. However, the block-block correlation in the paramagnetic phase is not strong enough to violate the Bell-CHSH inequality as the size of system becomes large. Furthermore, when the system violates the CHSH inequality, i.e., satisfies quantum non-locality, it needs to be entangled. On the other way, if the system obeys the CHSH inequality, it may be entangled or not. To gain further insight, the non-analytic and scaling behavior of QD and Bell non-locality have also been analyzed in detail and this phenomenon indicates that the behavior of the correlation can perfectly help one to observe the quantum critical properties of the model.

  7. Behavior of Early Warnings near the Critical Temperature in the Two-Dimensional Ising Model

    PubMed Central

    Morales, Irving O.; Landa, Emmanuel; Angeles, Carlos Calderon; Toledo, Juan C.; Rivera, Ana Leonor; Temis, Joel Mendoza; Frank, Alejandro

    2015-01-01

    Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of systems near critical points. These universal properties make it possible to estimate how far a system is from a critical threshold. Several early-warning signals have been reported in time series representing systems near catastrophic shifts. The proper understanding of these early-warnings may allow the prediction and perhaps control of these dramatic shifts in a wide variety of systems. In this paper we analyze this universal behavior for a system that is a paradigm of phase transitions, the Ising model. We study the behavior of the early-warning signals and the way the temporal correlations of the system increase when the system is near the critical point. PMID:26103513

  8. Analysis of spanning avalanches in the two-dimensional nonequilibrium zero-temperature random-field Ising model.

    PubMed

    Spasojević, Djordje; Janićević, Sanja; Knežević, Milan

    2014-01-01

    We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.

  9. Two-dimensional Ising transition through a technique from two-state opinion-dynamics models.

    PubMed

    Galam, Serge; Martins, André C R

    2015-01-01

    The Ising ferromagnetic model on a square lattice is revisited using the Galam unifying frame (GUF), set to investigate two-state opinion-dynamics models. When combined with Metropolis dynamics, an unexpected intermediate "dis/order" regime is found with the coexistence of two attractors associated, respectively, to an ordered and a disordered phases. The basin of attraction of initial conditions for the disordered phase attractor starts from zero size at a first critical temperature T(c1) to embody the total landscape of initial conditions at a second critical temperature T(c2), with T(c1)≈1.59 and T(c2)≈2.11 in J/k(B) units. It appears that T(c2) is close to the Onsager result T(c)≈2.27. The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at T(c2), reminiscent of the rather abrupt vanishing of the corresponding Onsager second-order transition. However, using Glauber dynamics combined with GUF does not yield the intermediate phase and instead the expected classical mean-field transition is recovered at T(c)≈3.09. Accordingly, although the "dis/order" regime produced by the GUF-Metropolis combination is not physical, it is an intriguing result to be understood. In particular the fact that Glauber and Metropolis dynamics yield so different results using GUF needs an explanation. The possibility of extending GUF to larger clusters is discussed. PMID:25679571

  10. Determination of critical linear lattice size for the four dimensional Ising model on the Creutz cellular automaton

    NASA Astrophysics Data System (ADS)

    Kizilirmak, Ganimet Mülazımoğlu

    2015-12-01

    The four-dimensional Ising model is simulated on the Creutz cellular automaton (CCA) near the infinite-lattice critical temperature for the lattice with the linear dimension 4 ⩽ L ⩽ 22. The temperature dependence of Binder parameter ( g L) are analyzed for the lattice with the linear dimension 4 ⩽ L ⩽ 22. In this study conducted highly detailed, two different types of behavior were determined as a result of varying linear lattice dimension. The infinite lattice critical temperatures are obtained to be T c = 6.6845 ± 0.0005 in interval 4 ⩽ L ⩽ 12 and T c = 6.6807 ± 0.0024 in interval 14 ⩽ L ⩽ 22. The finite and infinite lattice critical exponents for the order parameter, the magnetic susceptibility and the specific heat are computed from the results of simulations by using finite-size scaling relations. Critical linear lattice size have been identified as L = 14.

  11. Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model

    NASA Astrophysics Data System (ADS)

    Fytas, Nikolaos G.; Theodorakis, Panagiotis E.; Hartmann, Alexander K.

    2016-09-01

    We revisit the scaling behavior of the specific heat of the three-dimensional random-field Ising model with a Gaussian distribution of the disorder. Exact ground states of the model are obtained using graph-theoretical algorithms for different strengths 𝒩 = 268 3 spins. By numerically differentiating the bond energy with respect to h, a specific-heat-like quantity is obtained whose maximum is found to converge to a constant in the thermodynamic limit. Compared to a previous study following the same approach, we have studied here much larger system sizes with an increased statistical accuracy. We discuss the relevance of our results under the prism of a modified Rushbrooke inequality for the case of a saturating specific heat. Finally, as a byproduct of our analysis, we provide high-accuracy estimates of the critical field h c = 2.279(7) and the critical exponent of the correlation exponent ν = 1.37(1), in excellent agreement to the most recent computations in the literature.

  12. The finite-size scaling study of four-dimensional Ising model in the presence of external magnetic field

    NASA Astrophysics Data System (ADS)

    Merdan, Ziya; Kürkçü, Cihan; Öztürk, Mustafa K.

    2014-12-01

    The four-dimensional ferromagnetic Ising model in external magnetic field is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice, Tc χ ( ∞ ) = 6 , 680 (1) obtained for h = 0 agrees well with the values T c ( ∞ ) ≈ 6.68 obtained previously using different methods. Moreover, h = 0.00025 in our work also agrees with all the results obtained from h = 0 in the literature. However, there are no works for h ≠ 0 in the literature. The value of the field critical exponent (δ = 3.0136(3)) is in good agreement with δ = 3 which is obtained from scaling law of Widom. In spite of the finite-size scaling relations of | M L ( t ) | and χ L ( t ) for 0 ≤ h ≤ 0.001 are verified; however, in the cases of 0.0025 ≤ h ≤ 0.1 they are not verified.

  13. Graphene ripples as a realization of a two-dimensional Ising model: A scanning tunneling microscope study

    NASA Astrophysics Data System (ADS)

    Schoelz, J. K.; Xu, P.; Meunier, V.; Kumar, P.; Neek-Amal, M.; Thibado, P. M.; Peeters, F. M.

    2015-01-01

    Ripples in pristine freestanding graphene naturally orient themselves in an array that is alternately curved-up and curved-down; maintaining an average height of zero. Using scanning tunneling microscopy (STM) to apply a local force, the graphene sheet will reversibly rise and fall in height until the height reaches 60%-70% of its maximum at which point a sudden, permanent jump occurs. We successfully model the ripples as a spin-half Ising magnetic system, where the height of the graphene plays the role of the spin. The permanent jump in height, controlled by the tunneling current, is found to be equivalent to an antiferromagnetic-to-ferromagnetic phase transition. The thermal load underneath the STM tip alters the local tension and is identified as the responsible mechanism for the phase transition. Four universal critical exponents are measured from our STM data, and the model provides insight into the statistical role of graphene's unusual negative thermal expansion coefficient.

  14. Stable Degeneracies for Ising Models

    NASA Astrophysics Data System (ADS)

    Knauf, Andreas

    2016-10-01

    We introduce and consider the notion of stable degeneracies of translation invariant energy functions, taken at spin configurations of a finite Ising model. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction. We show that besides the symmetry-induced degeneracies, related to spin flip, translation and reflection, there exist additional stable degeneracies, due to more subtle symmetries. One such symmetry is the one of the Singer group of a finite projective plane. Others are described by combinatorial relations akin to trace identities. Our results resemble traits of the length spectrum for closed geodesics on a Riemannian surface of constant negative curvature. There, stable degeneracy is defined w.r.t. Teichmüller space as parameter space.

  15. Influence of the aspect ratio and boundary conditions on universal finite-size scaling functions in the athermal metastable two-dimensional random field Ising model.

    PubMed

    Navas-Portella, Víctor; Vives, Eduard

    2016-02-01

    This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂. PMID:26986310

  16. Dynamic hysteresis behaviors for the two-dimensional mixed spin (2, 5/2) ferrimagnetic Ising model in an oscillating magnetic field

    NASA Astrophysics Data System (ADS)

    Ertaş, Mehmet

    2015-09-01

    Keskin and Ertaş (2009) presented a study of the magnetic properties of a mixed spin (2, 5/2) ferrimagnetic Ising model within an oscillating magnetic field. They employed dynamic mean-field calculations to find the dynamic phase transition temperatures, the dynamic compensation points of the model and to present the dynamic phase diagrams. In this work, we extend the study and investigate the dynamic hysteresis behaviors for the two-dimensional (2D) mixed spin (2, 5/2) ferrimagnetic Ising model on a hexagonal lattice in an oscillating magnetic field within the framework of dynamic mean-field calculations. The dynamic hysteresis curves are obtained for both the ferromagnetic and antiferromagnetic interactions and the effects of the Hamiltonian parameters on the dynamic hysteresis behaviors are discussed in detail. The thermal behaviors of the coercivity and remanent magnetizations are also investigated. The results are compared with some theoretical and experimental works and a qualitatively good agreement is found. Finally, the dynamic phase diagrams depending on the frequency of an oscillating magnetic field in the plane of the reduced temperature versus magnetic field amplitude is examined and it is found that the dynamic phase diagrams display richer dynamic critical behavior for higher values of frequency than for lower values.

  17. 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

    2013-08-01

    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. PMID:23952393

  18. A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

    PubMed Central

    Takata, Kenta; Marandi, Alireza; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa

    2016-01-01

    Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances. PMID:27659312

  19. A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

    NASA Astrophysics Data System (ADS)

    Takata, Kenta; Marandi, Alireza; Hamerly, Ryan; Haribara, Yoshitaka; Maruo, Daiki; Tamate, Shuhei; Sakaguchi, Hiromasa; Utsunomiya, Shoko; Yamamoto, Yoshihisa

    2016-09-01

    Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

  20. Coupled modified baker's transformations for the Ising model.

    PubMed

    Sakaguchi, H

    1999-12-01

    An invertible coupled map lattice is proposed for the Ising model. Each elemental map is a modified baker's transformation, which is a two-dimensional map of X and Y. The time evolution of the spin variable is memorized in the binary representation of the Y variable. The temporal entropy and time correlation of the spin variable are calculated from the snapshot configuration of the Y variables.

  1. Transverse Ising model with multi-impurity

    NASA Astrophysics Data System (ADS)

    Huang, Xuchu; Yang, Zhihua

    2015-05-01

    We study the transverse Ising spin model with spin-1 impurities under the exact solution. We develop a universal method to deal with the multi-impurity problem by introducing a displacement quantity in the wave function and get a recursive formula to simplify the calculation of the partition function. This allows us to rigorously determine the impurity effects for a specific distribution of impurity in the thermodynamic limit. The low temperature behaviors are governed by the interplay between host and impurity excitations, and the quantum critical fluctuations around the critical point of the transverse Ising model are tuned by the transverse field and the concentration of impurity. However the impurity effects are limited, which depends on the host-impurity exchange interaction and the coupling strength of impurities.

  2. Dynamic phase transition in diluted Ising model

    NASA Astrophysics Data System (ADS)

    Chattopadhyay, Sourav; Gorai, Gopal; Santra, S. B.

    2015-06-01

    Dynamic phase transition in disordered Ising model in two dimensions has been studied in presence of external time dependent oscillating magnetic field applying Glauber Monte Carlo techniques. Dynamic phase transitions are identified estimating dynamic order parameter against temperature for different concentrations of disorder. For a given field strength and frequency for which there was no hysteresis, it is observed that disorder is able induce hysteresis in the system. Effect of increasing concentration of disorder on hysteresis loop area has also been studied.

  3. The hobbyhorse of magnetic systems: the Ising model

    NASA Astrophysics Data System (ADS)

    Ibarra-García-Padilla, Eduardo; Gerardo Malanche-Flores, Carlos; Poveda-Cuevas, Freddy Jackson

    2016-11-01

    In undergraduate statistical mechanics courses the Ising model always plays an important role because it is the simplest non-trivial model used to describe magnetic systems. The one-dimensional model is easily solved analytically, while the two-dimensional one can be solved exactly by the Onsager solution. For this reason, numerical simulations are usually used to solve the two-dimensional model. Keeping in mind that the two-dimensional model is the platform for studying phase transitions, it is usually an exercise in computational undergraduate courses because its numerical solution is relatively simple to implement and its critical exponents are perfectly known. The purpose of this article is to present a detailed numerical study of the second-order phase transition in the two-dimensional Ising model at an undergraduate level, allowing readers not only to compare the mean-field solution, the exact solution and the numerical one through a complete study of the order parameter, the correlation function and finite-size scaling, but to present the techniques, along with hints and tips, for solving it themselves. We present the elementary theory of phase transitions and explain how to implement Markov chain Monte Carlo simulations and perform them for different lattice sizes with periodic boundary conditions. Energy, magnetization, specific heat, magnetic susceptibility and the correlation function are calculated and the critical exponents determined by finite-size scaling techniques. The importance of the correlation length as the relevant parameter in phase transitions is emphasized.

  4. Thermal Ising transitions in the vicinity of two-dimensional quantum critical points

    NASA Astrophysics Data System (ADS)

    Hesselmann, S.; Wessel, S.

    2016-04-01

    The scaling of the transition temperature into an ordered phase close to a quantum critical point as well as the order parameter fluctuations inside the quantum critical region provide valuable information about universal properties of the underlying quantum critical point. Here, we employ quantum Monte Carlo simulations to examine these relations in detail for two-dimensional quantum systems that exhibit a finite-temperature Ising-transition line in the vicinity of a quantum critical point that belongs to the universality class of either (i) the three-dimensional Ising model for the case of the quantum Ising model in a transverse magnetic field on the square lattice or (ii) the chiral Ising transition for the case of a half-filled system of spinless fermions on the honeycomb lattice with nearest-neighbor repulsion. While the first case allows large-scale simulations to assess the scaling predictions to a high precision in terms of the known values for the critical exponents at the quantum critical point, for the later case, we extract values of the critical exponents ν and η , related to the order parameter fluctuations, which we discuss in relation to other recent estimates from ground-state quantum Monte Carlo calculations as well as analytical approaches.

  5. The Ising model in physics and statistical genetics.

    PubMed

    Majewski, J; Li, H; Ott, J

    2001-10-01

    Interdisciplinary communication is becoming a crucial component of the present scientific environment. Theoretical models developed in diverse disciplines often may be successfully employed in solving seemingly unrelated problems that can be reduced to similar mathematical formulation. The Ising model has been proposed in statistical physics as a simplified model for analysis of magnetic interactions and structures of ferromagnetic substances. Here, we present an application of the one-dimensional, linear Ising model to affected-sib-pair (ASP) analysis in genetics. By analyzing simulated genetics data, we show that the simplified Ising model with only nearest-neighbor interactions between genetic markers has statistical properties comparable to much more complex algorithms from genetics analysis, such as those implemented in the Allegro and Mapmaker-Sibs programs. We also adapt the model to include epistatic interactions and to demonstrate its usefulness in detecting modifier loci with weak individual genetic contributions. A reanalysis of data on type 1 diabetes detects several susceptibility loci not previously found by other methods of analysis.

  6. Three representations of the Ising model

    NASA Astrophysics Data System (ADS)

    Kruis, Joost; Maris, Gunter

    2016-10-01

    Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense.

  7. Three representations of the Ising model

    PubMed Central

    Kruis, Joost; Maris, Gunter

    2016-01-01

    Statistical models that analyse (pairwise) relations between variables encompass assumptions about the underlying mechanism that generated the associations in the observed data. In the present paper we demonstrate that three Ising model representations exist that, although each proposes a distinct theoretical explanation for the observed associations, are mathematically equivalent. This equivalence allows the researcher to interpret the results of one model in three different ways. We illustrate the ramifications of this by discussing concepts that are conceived as problematic in their traditional explanation, yet when interpreted in the context of another explanation make immediate sense. PMID:27698356

  8. 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

  9. 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.

  10. Exact ground states of large two-dimensional planar Ising spin glasses

    NASA Astrophysics Data System (ADS)

    Pardella, G.; Liers, F.

    2008-11-01

    Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 30002 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche approach.

  11. First-order and tricritical wetting transitions in the two-dimensional Ising model caused by interfacial pinning at a defect line.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt

    2014-08-01

    We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples. PMID:25215741

  12. First-order and tricritical wetting transitions in the two-dimensional Ising model caused by interfacial pinning at a defect line.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt

    2014-08-01

    We present a study of the critical behavior of the Blume-Capel model with three spin states (S=±1,0) confined between parallel walls separated by a distance L where competitive surface magnetic fields act. By properly choosing the crystal field (D), which regulates the density of nonmagnetic species (S=0), such that those impurities are excluded from the bulk (where D=-∞) except in the middle of the sample [where D(M)(L/2)≠-∞], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature (T(w)) versus the magnitude of the crystal field at the middle of the sample (D(M)), we observe curves of (first-) second-order wetting transitions for (small) high values of D(M). Theses lines meet in tricritical wetting points, i.e., (T(w)(tc),D(M)(tc)), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples.

  13. The Worm Process for the Ising Model is Rapidly Mixing

    NASA Astrophysics Data System (ADS)

    Collevecchio, Andrea; Garoni, Timothy M.; Hyndman, Timothy; Tokarev, Daniel

    2016-09-01

    We prove rapid mixing of the worm process for the zero-field ferromagnetic Ising model, on all finite connected graphs, and at all temperatures. As a corollary, we obtain a fully-polynomial randomized approximation scheme for the Ising susceptibility, and for a certain restriction of the two-point correlation function.

  14. Applying Tabu Search to the Two-Dimensional Ising Spin Glass

    NASA Astrophysics Data System (ADS)

    Laguna, Manuel; Laguna, Pablo

    A variety of problems in statistical physics, such as Ising-like systems, can be modeled as integer programs. Physicists have relied mostly on Monte Carlo methods to find approximate solutions to these computationally difficult problems. In some cases, optimal solutions to relatively small problems have been found using standard optimization techniques, e.g., cutting plane and branch-and-bound algorithms. Motivated by the success of tabu search (TS) in finding optimal or near-optimal solutions to combinatorial optimization problems in a number of different settings, we study the application of this methodology to Ising-like systems. Particularly, we develop a TS method to find ground states of two-dimensional spin glasses. Our method performs a search at different levels of resolution in the spin lattice, and it is designed to obtain optimal or near-optimal solutions to problem instances with several different characteristics. Results are reported for computational experiments with up to 64×64 lattices.

  15. Ising tricriticality in the extended Hubbard model with bond dimerization

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

    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.

  16. Phase transitions in a three-dimensional kinetic spin-1/2 Ising model with random field: effective-field-theory study.

    PubMed

    Costabile, Emanuel; de Sousa, J Ricardo

    2012-01-01

    The dynamical phase transitions of the kinetic Ising model in the presence of a random magnetic field with a bimodal probability distribution is studied by using effective-field theory (EFT) with correlations. We have used a Glauber-type stochastic dynamic to describe the time evolution of the system, where the system strongly depends on the H≡√(c) root mean square deviation of the magnetic field. The EFT dynamic equation is given for the simple cubic lattice (z=6), and the dynamic order parameter is calculated. The system presents ferromagnetic and paramagnetic states for low and high temperatures, respectively. Our results predict first-order transitions at low temperatures and large disorder strengths, which corresponds to the existence of a nonequilibrium tricritical point (TCP) in a phase diagram in the T-H plane. We compare the results with the equilibrium phase diagram, where only the first-order line is different. Our qualitative results are compatible with recent Monte Carlo simulations.

  17. Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models: Ising Model and Monodromy Preserving Deformation

    NASA Astrophysics Data System (ADS)

    Miwa, Tetsuji

    2013-03-01

    Studies on integrable models in statistical mechanics and quantum field theory originated in the works of Bethe on the one-dimensional quantum spin chain and the work of Onsager on the two-dimensional Ising model. I will talk on the discovery in 1977 of the link between quantum field theory in the scaling limit of the two-dimensional Ising model and the theory of monodromy preserving linear ordinary differential equations. This work was the staring point of our journey with Michio Jimbo in integrable models, the journey which finally led us to the exact results on the correlation functions of quantum spin chains in 1992.

  18. Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: A short-time dynamics study.

    PubMed

    Horowitz, C M; Bab, M A; Mazzini, M; Rubio Puzzo, M L; Saracco, G P

    2015-10-01

    The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5≤δ≤1.3, where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5≤δ≤1.2 indicate that the phase transition line between the h=1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

  19. Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices

    NASA Astrophysics Data System (ADS)

    Ananikian, N. S.; Ananikyan, L. N.; Chakhmakhchyan, L. A.

    2011-09-01

    The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.

  20. 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

  1. Toward an Ising model of cancer and beyond

    NASA Astrophysics Data System (ADS)

    Torquato, Salvatore

    2011-02-01

    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 the research 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 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 study 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. We then describe how to incorporate angiogenesis as well as the heterogeneous and confined environment in which a tumor grows in the CA model. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently discussed. 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

  2. Ising-model description of long-range correlations in DNA sequences

    NASA Astrophysics Data System (ADS)

    Colliva, A.; Pellegrini, R.; Testori, A.; Caselle, M.

    2015-05-01

    We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 103 and 106 bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction between distant portions of the DNA chain which led to the DNA structure that we observe today in higher eukaryotes.

  3. Long range Ising model for credit risk modeling

    NASA Astrophysics Data System (ADS)

    Molins, Jordi; Vives, Eduard

    2005-07-01

    Within the framework of maximum entropy principle we show that the finite-size long-range Ising model is the adequate model for the description of homogeneous credit portfolios and the computation of credit risk when default correlations between the borrowers are included. The exact analysis of the model suggest that when the correlation increases a first-order-like transition may occur inducing a sudden risk increase.

  4. Exponentially improved classical and quantum algorithms for three-body Ising models

    NASA Astrophysics Data System (ADS)

    Van den Nest, M.; Dür, W.

    2014-01-01

    We present an algorithm to approximate partition functions of three-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely, the color codes. The algorithm performance (in achievable accuracy) is exponentially better than other approaches that employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.

  5. Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions

    NASA Astrophysics Data System (ADS)

    Alves, G. A.; Vasconcelos, M. S.; Alves, T. F. A.

    2016-04-01

    We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter qEA, the magnetic susceptibility χ , and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β ,γ , and ν . In the low-temperature limit we obtained a spin-glass phase with critical temperature around Tc≈2.274 , and the critical exponents β ,γ , and ν , indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model.

  6. Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions.

    PubMed

    Alves, G A; Vasconcelos, M S; Alves, T F A

    2016-04-01

    We address the study of quasiperiodic interactions on a square lattice by using an Ising model with ferromagnetic and antiferromagnetic exchange interactions following a quasiperiodic Fibonacci sequence in both directions of a square lattice. We applied the Monte Carlo method, together with the Metropolis algorithm, to calculate the thermodynamic quantities of the system. We obtained the Edwards-Anderson order parameter q_{EA}, the magnetic susceptibility χ, and the specific heat c in order to characterize the universality class of the phase transition. We also use the finite size scaling method to obtain the critical temperature of the system and the critical exponents β,γ, and ν. In the low-temperature limit we obtained a spin-glass phase with critical temperature around T_{c}≈2.274, and the critical exponents β,γ, and ν, indicating that the quasiperiodic order induces a change in the universality class of the system. Also, we discovered a spin-glass ordering in a two-dimensional system which is rare and, as far as we know, the unique example is an under-frustrated Ising model. PMID:27176258

  7. Self-organizing Ising model of financial markets

    NASA Astrophysics Data System (ADS)

    Zhou, W.-X.; Sornette, D.

    2007-01-01

    We study a dynamical Ising-like model of agents' opinions (buy or sell) with learning, in which the coupling coefficients are re-assessed continuously in time according to how past external news (time-varying magnetic field) have explained realized market returns. By combining herding, the impact of external news and private information, we find that the stylized facts of financial markets are reproduced only when agents misattribute the success of news to predict return to herding effects, thereby providing positive feedbacks leading to the model functioning close to the Ising critical point.

  8. Interacting damage models mapped onto ising and percolation models

    SciTech Connect

    Toussaint, Renaud; Pride, Steven R.

    2004-03-23

    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 the 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

  9. Geometrical clusters of Darcy's reservoir model and Ising universality class

    NASA Astrophysics Data System (ADS)

    Najafi, M. N.; Ghaedi, M.

    2015-06-01

    In this paper the geometrical features of the fluid propagation in two-dimensional petroleum reservoir described by Darcy equations are studied. The porous media are considered to be tuned by the occupancy parameter p being the probability that a pore is occupied. We analyze the statistical geometrical observables of the Darcy model. To this end we let the water to be injected into random sites of the porous media and solve numerically the Darcy equations to describe the flow motion pattern, using the control volume finite difference (CVFD) method. The fractal dimension of the frontier of the avalanches (defined as the set of the sites through which the fluid passed) and the distribution functions of gyration radius, loop length and cluster mass are numerically obtained revealing that at p =pc (the critical occupancy parameter above which there is definitely a spanning cluster in the system) this model lies within a universality class compatible with the Ising model. We observe that for p >pc, although the model shows critical behaviors, this duality is broken. The mentioned exponents are reported in this paper.

  10. Random field Ising model and community structure in complex networks

    NASA Astrophysics Data System (ADS)

    Son, S.-W.; Jeong, H.; Noh, J. D.

    2006-04-01

    We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field Bs = +∞, Bt = -∞, and Bi≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)

  11. 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.

  12. Duality Between Spin Networks and the 2D Ising Model

    NASA Astrophysics Data System (ADS)

    Bonzom, Valentin; Costantino, Francesco; Livine, Etera R.

    2016-06-01

    The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.

  13. Topological defects on the lattice: I. The Ising model

    NASA Astrophysics Data System (ADS)

    Aasen, David; Mong, Roger S. K.; Fendley, Paul

    2016-09-01

    In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.

  14. Topological defects on the lattice: I. The Ising model

    NASA Astrophysics Data System (ADS)

    Aasen, David; Mong, Roger S. K.; Fendley, Paul

    2016-09-01

    In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.

  15. Solution of the antiferromagnetic Ising model on a tetrahedron recursive lattice.

    PubMed

    Jurčišinová, E; Jurčišin, M

    2014-03-01

    We consider the antiferromagnetic spin-1/2 Ising model on the recursive tetrahedron lattice on which two elementary tetrahedrons are connected at each site. The model represents the simplest approximation of the antiferromagnetic Ising model on the real three-dimensional tetrahedron lattice which takes into account effects of frustration. An exact analytical solution of the model is found and discussed. It is shown that the model exhibits neither the first-order nor the second-order phase transitions. A detailed analysis of the magnetization of the model in the presence of the external magnetic field is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found.

  16. Periodic Striped Ground States in Ising Models with Competing Interactions

    NASA Astrophysics Data System (ADS)

    Giuliani, Alessandro; Seiringer, Robert

    2016-11-01

    We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c ( p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2 d and J in a left neighborhood of J c ( p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes ( d = 2) or slabs ( d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

  17. Critical behavior of the Ising model on random fractals.

    PubMed

    Monceau, Pascal

    2011-11-01

    We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.

  18. Periodic Striped Ground States in Ising Models with Competing Interactions

    NASA Astrophysics Data System (ADS)

    Giuliani, Alessandro; Seiringer, Robert

    2016-06-01

    We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J c (p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J c (p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

  19. Two Dimensional Ising Superconductivity in Gated MoS2

    NASA Astrophysics Data System (ADS)

    Yuan, Noah; Lu, Jianming; Law, Kam Tuen; Zheliuk, Oleksandr; Leermakers, Inge; Zeitler, Ulrich; Ye, Jianting

    The Zeeman effect, which is usually considered to be detrimental to superconductivity, can surprisingly protect the superconducting states created by gating a layered transition metal dichalcogenide. This effective Zeeman field, which is originated from intrinsic spin orbit coupling induced by breaking in-plane inversion symmetry, can reach nearly a hundred Tesla in magnitude. It strongly pins the spin orientation of the electrons to the out-of-plane directions and protects the superconductivity from being destroyed by an in-plane external magnetic field. In magnetotransport experiments of ionic-gate MoS2 transistors, where gating prepares individual superconducting state with different carrier doping, we indeed observe a spin-protected superconductivity by measuring an in-plane critical field Bc 2 far beyond the Pauli paramagnetic limit. The gating-enhanced Bc 2 is more than an order of magnitude larger compared to the bulk superconducting phases where the effective Zeeman field is weakened by interlayer coupling. Our study gives the first experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

  20. Quenched Central Limit Theorems for the Ising Model on Random Graphs

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    The main goal of the paper is to prove central limit theorems for the magnetization rescaled by for the Ising model on random graphs with N vertices. Both random quenched and averaged quenched measures are considered. We work in the uniqueness regime or and , where is the inverse temperature, is the critical inverse temperature and B is the external magnetic field. In the random quenched setting our results apply to general tree-like random graphs (as introduced by Dembo, Montanari and further studied by Dommers and the first and third author) and our proof follows that of Ellis in . For the averaged quenched setting, we specialize to two particular random graph models, namely the 2-regular configuration model and the configuration model with degrees 1 and 2. In these cases our proofs are based on explicit computations relying on the solution of the one dimensional Ising models.

  1. A MATLAB GUI to study Ising model phase transition

    NASA Astrophysics Data System (ADS)

    Thornton, Curtislee; Datta, Trinanjan

    We have created a MATLAB based graphical user interface (GUI) that simulates the single spin flip Metropolis Monte Carlo algorithm. The GUI has the capability to study temperature and external magnetic field dependence of magnetization, susceptibility, and equilibration behavior of the nearest-neighbor square lattice Ising model. Since the Ising model is a canonical system to study phase transition, the GUI can be used both for teaching and research purposes. The presence of a Monte Carlo code in a GUI format allows easy visualization of the simulation in real time and provides an attractive way to teach the concept of thermal phase transition and critical phenomena. We will also discuss the GUI implementation to study phase transition in a classical spin ice model on the pyrochlore lattice.

  2. Phase transition of the Ising model on a fractal lattice.

    PubMed

    Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi

    2016-01-01

    The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry. PMID:26871057

  3. Precision islands in the Ising and O( N ) models

    NASA Astrophysics Data System (ADS)

    Kos, Filip; Poland, David; Simmons-Duffin, David; Vichi, Alessandro

    2016-08-01

    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 ɛ , λ σσɛ , λ ɛɛɛ ) = (0 .5181489(10) , 1 .412625(10) , 1 .0518537(41) , 1 .532435(19) , give the most precise determinations of these quantities to date.

  4. Ising model observables and non-backtracking walks

    SciTech Connect

    Helmuth, Tyler

    2014-08-15

    This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph G and the set of non-backtracking walks on G. The techniques used also give formulas for spin-spin correlation functions in terms of non-backtracking walks. The main tools used are Viennot's theory of heaps of pieces and turning numbers on surfaces.

  5. The Signed Loop Approach to the Ising Model: Foundations and Critical Point

    NASA Astrophysics Data System (ADS)

    Kager, Wouter; Lis, Marcin; Meester, Ronald

    2013-07-01

    The signed loop approach is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.

  6. High-temperature expansions of the higher susceptibilities for the Ising model in general dimension d.

    PubMed

    Butera, P; Pernici, M

    2012-07-01

    The high-temperature expansion coefficients of the ordinary and the higher susceptibilities of the spin-1/2 nearest-neighbor Ising model are calculated exactly up to the 20th order for the general d-dimensional (hyper)simple-cubical lattices. These series are analyzed to study the dependence of critical parameters on the lattice dimensionality. Using the general d expression of the ordinary susceptibility, we have more than doubled the length of the existing series expansion of the critical temperature in powers of 1/d.

  7. Droplets pinned at chemically inhomogenous substrates: A simulation study of the two-dimensional Ising case.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt

    2016-05-01

    As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature T_{w} of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches T_{w} from below are studied. In accord with theoretical predictions, for T>T_{w} the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b^{1/2}). So, the area of the droplet is proportional to b^{3/2}, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied. PMID:27300962

  8. Droplets pinned at chemically inhomogenous substrates: A simulation study of the two-dimensional Ising case.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V; Binder, Kurt

    2016-05-01

    As a simplified model of a liquid nanostripe adsorbed on a chemically structured substrate surface, a two-dimensional Ising system with two boundaries at which surface fields act is studied. At the upper boundary, the surface field is uniformly negative, while at the lower boundary (a distance L apart), the surface field is negative only outside a range of extension b, where a positive surface stabilizes a droplet of the phase with positive magnetization for temperatures T exceeding the critical temperature T_{w} of the wetting transition of this model. We investigate the local order parameter profiles across the droplet, both in the directions parallel and perpendicular to the substrate, varying both b and T. Also, precursor effects to droplet formation as T approaches T_{w} from below are studied. In accord with theoretical predictions, for T>T_{w} the droplet is found to have the shape of a semiellipse, where the width (distance of the interface from the substrate) scale is proportional to b (b^{1/2}). So, the area of the droplet is proportional to b^{3/2}, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.

  9. Self-overlap as a method of analysis in Ising models.

    PubMed

    Ferrera, A; Luque, B; Lacasa, L; Valero, E

    2007-06-01

    The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model--amongst many others--but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler.

  10. The scaling limit of the energy correlations in non-integrable Ising models

    NASA Astrophysics Data System (ADS)

    Giuliani, Alessandro; Greenblatt, Rafael L.; Mastropietro, Vieri

    2012-09-01

    We obtain an explicit expression for the multipoint energy correlations of a non-solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength λ, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis, and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in λ. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit bounds on the speed of convergence to the scaling limit are derived.

  11. Exact results for a random frustrated Ising model on the Kagome lattice

    SciTech Connect

    Giacomini, H.J.; Riera, J.A.

    1987-11-01

    The authors perform a slight modification of the decoration-decimation transformation which allows us to map the homogeneous Ising model on the honeycomb lattice on an inhomogeneous Ising model on the Kagome lattice. Then, we obtain exact results for a class of random bond Ising model on the Kagome lattice with competing interactions and show that the different types of frustration make the critical point of the pure model disappear.

  12. 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.

  13. Impurity effects of transverse Ising model with multi-impurity

    NASA Astrophysics Data System (ADS)

    Huang, Xuchu; Yang, Zhihua

    2015-02-01

    We study the transverse Ising spin model with multi-impurity under the exact solution. The influence mechanisms of the concentration, configuration, impurity-inducing-interaction are investigated through the deformation energy, long-range order and the specific heat. It reveals a way that the impurities have crucial effects on the magnetic order of the system, which can be used to scale the order-disorder transition. In particular, the change of the exchange coupling interaction or magnetic field can lead to the deviation of the phase point. Moreover, the impurity excitation cannot be neglected in thermodynamic properties even though the concentration is only a few percent.

  14. 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.

  15. Globally nilpotent differential operators and the square Ising model

    NASA Astrophysics Data System (ADS)

    Bostan, A.; Boukraa, S.; Hassani, S.; Maillard, J.-M.; Weil, J.-A.; Zenine, N.

    2009-03-01

    We recall various multiple integrals with one parameter, related to the isotropic square Ising model, and corresponding, respectively, to the n-particle contributions of the magnetic susceptibility, to the (lattice) form factors, to the two-point correlation functions and to their λ-extensions. The univariate analytic functions defined by these integrals are holonomic and even G-functions: they satisfy Fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties. We recall the explicit forms, found in previous work, of these Fuchsian equations, as well as their Russian-doll and direct sum structures. These differential operators are selected Fuchsian linear differential operators, and their remarkable properties have a deep geometrical origin: they are all globally nilpotent, or, sometimes, even have zero p-curvature. We also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known. Focusing on the factorized parts of all these operators, we find out that the global nilpotence of the factors (resp. p-curvature nullity) corresponds to a set of selected structures of algebraic geometry: elliptic curves, modular curves, curves of genus five, six,..., and even a remarkable weight-1 modular form emerging in the three-particle contribution χ(3) of the magnetic susceptibility of the square Ising model. Noticeably, this associated weight-1 modular form is also seen in the factors of the differential operator for another n-fold integral of the Ising class, Φ(3)H, for the staircase polygons counting, and in Apéry's study of ζ(3). G-functions naturally occur as solutions of globally nilpotent operators. In the case where we do not have G-functions, but Hamburger functions (one irregular singularity at 0 or ∞) that correspond to the confluence of singularities in the scaling limit, the p-curvature is also found to verify new

  16. Oscillating hysteresis in the q-neighbor Ising model.

    PubMed

    Jȩdrzejewski, Arkadiusz; Chmiel, Anna; Sznajd-Weron, Katarzyna

    2015-11-01

    We modify the kinetic Ising model with Metropolis dynamics, allowing each spin to interact only with q spins randomly chosen from the whole system, which corresponds to the topology of a complete graph. We show that the model with q≥3 exhibits a phase transition between ferromagnetic and paramagnetic phases at temperature T*, which linearly increases with q. Moreover, we show that for q=3 the phase transition is continuous and that it is discontinuous for larger values of q. For q>3, the hysteresis exhibits oscillatory behavior-expanding for even values of q and shrinking for odd values of q. Due to the mean-field-like nature of the model, we are able to derive the analytical form of transition probabilities and, therefore, calculate not only the probability density function of the order parameter but also precisely determine the hysteresis and the effective potential showing stable, unstable, and metastable steady states. Our results show that a seemingly small modification of the kinetic Ising model leads not only to the switch from a continuous to a discontinuous phase transition, but also to an unexpected oscillating behavior of the hysteresis and a puzzling phenomenon for q=5, which might be taken as evidence for the so-called mixed-order phase transition.

  17. Scaling and super-universality in the coarsening dynamics of the 3D random field Ising model

    NASA Astrophysics Data System (ADS)

    Aron, Camille; Chamon, Claudio; Cugliandolo, Leticia F.; Picco, Marco

    2008-05-01

    We study the coarsening dynamics of the three-dimensional random field Ising model using Monte Carlo numerical simulations. We test the dynamic scaling and super-scaling properties of global and local two-time observables. We treat in parallel the three-dimensional Edward-Anderson spin glass and we recall results on Lennard-Jones mixtures and colloidal suspensions to highlight the common and different out of equilibrium properties of these glassy systems.

  18. Spin-1 Ising model on tetrahedron recursive lattices: Exact results

    NASA Astrophysics Data System (ADS)

    Jurčišinová, E.; Jurčišin, M.

    2016-11-01

    We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z = 6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.

  19. Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study

    SciTech Connect

    Dusuel, Sebastien; Kamfor, Michael; Schmidt, Kai Phillip; Thomale, Ronny; Vidal, Julien

    2010-02-01

    We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.

  20. The Ising Model Applied on Chronification of Pain

    PubMed Central

    2016-01-01

    This is a hypothesis-article suggesting an entirely new framework for understanding and treating longstanding pain. Most medical and psychological models are described with boxes and arrows. Such models are of little clinical and explanatory use when describing the phenomenon of chronification of pain due to unknown causes. To date no models that have been provided - and tested in a scientific satisfactory way - lays out a plan for specific assessment due to a specific causal explanation, and in the end serves the clinicians, patients and researcher with tools on how to address the specific pain condition to every individual pain patient's condition. By applying the Ising model (from physics) on the phenomenon of chronification of pain, one is able to detangle all these factors, and thus have a model that both suggests an explanation of the condition and outlines how one might target the treatment of chronic pain patients with the use of network science. PMID:26398917

  1. Quantum cluster algorithm for frustrated Ising models in a transverse field

    NASA Astrophysics Data System (ADS)

    Biswas, Sounak; Rakala, Geet; Damle, Kedar

    2016-06-01

    Working within the stochastic series expansion framework, we introduce and characterize a plaquette-based quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this algorithm, we show that a relatively small ferromagnetic next-nearest-neighbor coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic three-sublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.

  2. Emergent Ising degrees of freedom in the J1-J2-J3 model for the iron tellurides

    NASA Astrophysics Data System (ADS)

    Zhang, Guanghua; Fernandes, Rafael; Flint, Rebecca

    The iron-telluride family of superconductors form a double-stripe [ Q = (π / 2 , π / 2) ] magnetic order, which can be 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. Via their coupling to the lattice, they give rise to a monoclinic distortion and to two non-uniform lattice distortions with wave-vector (π , π) . Because the ground state is four-fold degenerate (mod rotations in spin space), only two of these Ising order parameters are independent. Here we introduce an effective field theory to treat all Ising order parameters, as well as magnetic order. All three transitions (corresponding to the condensations of two Ising 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.

  3. Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

    NASA Astrophysics Data System (ADS)

    Pan, Xue; Chen, Li-Zhu; Wu, Yuan-Fang

    2016-09-01

    The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign. Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)

  4. 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.

  5. Reentrance of disorder in the anisotropic shuriken Ising model

    NASA Astrophysics Data System (ADS)

    Pohle, Rico; Benton, Owen; Jaubert, L. D. C.

    2016-07-01

    Frustration is often a key ingredient for reentrance mechanisms. Here we study the frustrated anisotropic shuriken Ising model, where it is possible to extend the notion of reentrance between disordered phases, i.e., in absence of phase transitions. By tuning the anisotropy of the lattice, we open a window in the phase diagram where magnetic disorder prevails down to zero temperature, in a classical analogy with a quantum critical point. In this region, the competition between multiple disordered ground states gives rise to a double crossover where both the low- and high-temperature regimes are less correlated than the intervening classical spin liquid. This reentrance of disorder is characterized by an entropy plateau and a multistep Curie law crossover. Our theory is developed based on Monte Carlo simulations, analytical Husimi-tree calculations and an exact decoration-iteration transformation. Its relevance to experiments, in particular, artificial lattices, is discussed.

  6. Long-range Ising and Kitaev models: phases, correlations and edge modes

    NASA Astrophysics Data System (ADS)

    Vodola, Davide; Lepori, Luca; Ercolessi, Elisa; Pupillo, Guido

    2016-01-01

    We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance r as 1/{r}α , as well as a related class of fermionic Hamiltonians that generalize the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents α, based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for α ≲ 1, while connected correlation functions can decay with a hybrid exponential and power-law behavior, with a power that is α-dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every α. Along the critical lines, for all models breaking of conformal symmetry is argued at low enough α. For the fermionic models we show that the edge modes, massless for α ≳ 1, can acquire a mass for α \\lt 1. The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

  7. Phase Transitions for Quantum Markov Chains Associated with Ising Type Models on a Cayley Tree

    NASA Astrophysics Data System (ADS)

    Mukhamedov, Farrukh; Barhoumi, Abdessatar; Souissi, Abdessatar

    2016-05-01

    The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting.

  8. Scaling of the largest dynamical barrier in the one-dimensional long-range Ising spin glass

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile; Garel, Thomas

    2014-01-01

    The long-range one-dimensional Ising spin glass with random couplings decaying as J(r )∝r-σ presents a spin-glass phase Tc(σ)>0 for 0≤σ<1 (the limit σ =0 corresponds to the mean-field Sherrington-Kirkpatrick model). We use the eigenvalue method introduced in our previous work (C. Monthus and T. Garel, J. Stat. Mech. 2009, P12017) to measure the equilibrium time teq(N ) at temperature T =Tc(σ)/2 as a function of the number N of spins. We find the activated scaling lnteq(N )¯˜Nψ with the same barrier exponent ψ ≃0.33 in the whole region 0≤σ<1.

  9. LETTER TO THE EDITOR: Magnetic correlation length and universal amplitude of the lattice ? Ising model

    NASA Astrophysics Data System (ADS)

    Batchelor, M. T.; Seaton, K. A.

    1997-08-01

    The perturbation approach is used to derive the exact correlation length 0305-4470/30/15/001/img6 of the dilute 0305-4470/30/15/001/img7 lattice models in regimes 1 and 2 for L odd. In regime 2 the 0305-4470/30/15/001/img8 model is the 0305-4470/30/15/001/img9 lattice realization of the two-dimensional Ising model in a magnetic field h at 0305-4470/30/15/001/img10. When combined with the singular part 0305-4470/30/15/001/img11 of the free energy the result for the 0305-4470/30/15/001/img8 model gives the universal amplitude 0305-4470/30/15/001/img13 as 0305-4470/30/15/001/img14 in precise agreement with the result obtained by Delfino and Mussardo via the form-factor bootstrap approach.

  10. A simulation of the mixed spin 3-spin 3/2 ferrimagnetic Ising model

    NASA Astrophysics Data System (ADS)

    Özkan, Aycan

    2016-01-01

    The mixed spin 3-spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals -4 ≤ DA/J ≤ 8 and -4 ≤ DB/J ≤ 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through DA/J = 2 at kT/J = 0. The values of the critical exponents (ν, α , β and γ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected DA/J values (-2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model (ν = 1, α = α‧ = 0, β = 0.125, β‧ = 0.875 and γ = γ‧ = 1.75).

  11. Next nearest neighbour Ising models on random graphs

    NASA Astrophysics Data System (ADS)

    Raymond, Jack; Wong, K. Y. Michael

    2012-09-01

    This paper develops results for the next nearest neighbour Ising model on random graphs. Besides being an essential ingredient in classic models for frustrated systems, second neighbour interactions arise naturally in several applications, such as the colour diversity problem and graphical games. We demonstrate ensembles of random graphs, including regular connectivity graphs, that have a periodic variation of free energy, with either the ratio of nearest to next nearest couplings, or the mean number of nearest neighbours. When the coupling ratio is integer then paramagnetic phases can be found at zero temperature. This is shown to be related to the locked or unlocked nature of the interactions. For anti-ferromagnetic couplings, spin glass phases are demonstrated at low temperature. The interaction structure is formulated as a factor graph, the solution on a tree is developed. The replica symmetric and energetic one-step replica symmetry breaking solution is developed using the cavity method. We calculate within these frameworks the phase diagram and demonstrate the existence of dynamical transitions at zero temperature for cases of anti-ferromagnetic coupling on regular and inhomogeneous random graphs.

  12. Inhomogeneous and Self-Organized Temperature in Schelling-Ising Model

    NASA Astrophysics Data System (ADS)

    Müller, Katharina; Schulze, Christian; Stauffer, Dietrich

    The Schelling model of 1971 is a complicated version of a square-lattice Ising model at zero temperature, to explain urban segregation, based on the neighbor preferences of the residents, without external reasons. Various versions between Ising and Schelling models give about the same results. Inhomogeneous "temperatures" T do not change the results much, while a feedback between segregation and T leads to a self-organization of an average T.

  13. Entanglement and quantum phase transition in the Heisenberg—Ising model

    NASA Astrophysics Data System (ADS)

    Tan, Xiao-Dong; Jin, Bai-Qi; Gao, Wei

    2013-02-01

    We use the quantum renormalization-group (QRG) method to study the entanglement and quantum phase transition (QPT) in the one-dimensional spin-1/2 Heisenberg—Ising model [Lieb E, Schultz T and Mattis D 1961 Ann. Phys. (N.Y.) 16 407]. We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations. We also investigate the scaling behavior of the system close to the quantum critical point, which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size. Also, the first derivative of concurrence between two blocks diverges at the quantum critical point, which is directly associated with the divergence of the correlation length.

  14. Spreadsheet analysis of stability and meta-stability of low-dimensional magnetic particles using the Ising approach

    NASA Astrophysics Data System (ADS)

    Ehrmann, Andrea; Blachowicz, Tomasz; Zghidi, Hafed

    2015-05-01

    Modelling hysteresis behaviour, as it can be found in a broad variety of dynamical systems, can be performed in different ways. An elementary approach, applied for a set of elementary cells, which uses only two possible states per cell, is the Ising model. While such Ising models allow for a simulation of many systems with sufficient accuracy, they nevertheless depict some typical features which must be taken into account with proper care, such as meta-stability or the externally applied field sweeping speed. This paper gives a general overview of recent results from Ising models from the perspective of a didactic model, based on a 2D spreadsheet analysis, which can be used also for solving general scientific problems where direct next-neighbour interactions take place.

  15. The scaling window of the 5D Ising model with free boundary conditions

    NASA Astrophysics Data System (ADS)

    Lundow, P. H.; Markström, K.

    2016-10-01

    The five-dimensional Ising model with free boundary conditions has recently received a renewed interest in a debate concerning the finite-size scaling of the susceptibility near the critical temperature. We provide evidence in favour of the conventional scaling picture, where the susceptibility scales as L2 inside a critical scaling window of width 1 /L2. Our results are based on Monte Carlo data gathered on system sizes up to L = 79 (ca. three billion spins) for a wide range of temperatures near the critical point. We analyse the magnetisation distribution, the susceptibility and also the scaling and distribution of the size of the Fortuin-Kasteleyn cluster containing the origin. The probability of this cluster reaching the boundary determines the correlation length, and its behaviour agrees with the mean field critical exponent δ = 3, that the scaling window has width 1 /L2.

  16. Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model

    NASA Astrophysics Data System (ADS)

    Rotskoff, Grant M.; Crooks, Gavin E.

    2015-12-01

    A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines. Recent work has shown that a system driven out of equilibrium by a linear response protocol is endowed with a Riemannian metric related to generalized susceptibilities, and that geodesics on this manifold are the nonequilibrium control protocols with the lowest achievable dissipation. While this elegant mathematical framework has inspired numerous studies of exactly solvable systems, no description of the thermodynamic geometry yet exists when the metric cannot be derived analytically. Herein, we numerically construct the dynamic metric of the two-dimensional Ising model in order to study optimal protocols for reversing the net magnetization.

  17. 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.

  18. 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.

  19. Numerically exact solvable random-bond Ising model

    NASA Astrophysics Data System (ADS)

    Morgenstern, I.

    1981-06-01

    Exact free energies are calculated numerically for a L×L-Ising lattice ( L≦800) with constant nearest neighbour coupling between adjacent columns and random n.n. coupling between adjacent rows. For the latter a gaussian and a double-peaked δ-distribution are investigated. The result should be useful as a check of the controversially discussed replica trick [1]. In agreement with the numerical treatment a mean field approximation shows a transition to a spinglass phase.

  20. Ising spins on randomly multi-branched Husimi square lattice: Thermodynamics and phase transition in cross-dimensional range

    NASA Astrophysics Data System (ADS)

    Huang, Ran

    2016-10-01

    An inhomogeneous random recursive lattice is constructed from the multi-branched Husimi square lattice. The number of repeating units connected on one vertex is randomly set to be 2 or 3 with a fixed ratio P2 or P3 with P2 +P3 = 1. The lattice is designed to describe complex thermodynamic systems with variable coordinating neighbors, e.g. the asymmetric range around the surface of a bulk system. Classical ferromagnetic spin-1 Ising model is solved on the lattice to achieve an annealed solution via the local exact calculation technique. The model exhibits distinct spontaneous magnetization similar to the deterministic system, with however rigorous thermal fluctuations and significant singularities on the entropy behavior around the critical temperature, indicating a complex superheating frustration in the cross-dimensional range induced by the stochasticity. The critical temperature was found to be exponentially correlated to the structural ratio P with the coefficient fitted as 0.53187, while the ground state energy presents linear correlation to P, implying a well-defined average property according to the structural ratio.

  1. Exact solution of the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice

    NASA Astrophysics Data System (ADS)

    Strečka, Jozef

    2006-01-01

    A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4 8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.

  2. 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.

  3. Finite-size scaling of the magnetization probability density for the critical Ising model in slab geometry

    NASA Astrophysics Data System (ADS)

    Lopes Cardozo, David; Holdsworth, Peter C. W.

    2016-04-01

    The magnetization probability density in d  =  2 and 3 dimensional Ising models in slab geometry of volume L\\paralleld-1× {{L}\\bot} is computed through Monte-Carlo simulation at the critical temperature and zero magnetic field. The finite-size scaling of this distribution and its dependence on the system aspect-ratio ρ =\\frac{{{L}\\bot}}{{{L}\\parallel}} and boundary conditions are discussed. In the limiting case ρ \\to 0 of a macroscopically large slab ({{L}\\parallel}\\gg {{L}\\bot} ) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.

  4. 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. PMID:24875470

  5. 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.

  6. 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.

  7. Canonical vs. micro-canonical sampling methods in a 2D Ising model

    SciTech Connect

    Kepner, J.

    1990-12-01

    Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs.

  8. Self-Organizing Two-Temperature Ising Model Describing Human Segregation

    NASA Astrophysics Data System (ADS)

    Ódor, Géza

    A two-temperature Ising-Schelling model is introduced and studied for describing human segregation. The self-organized Ising model with Glauber kinetics simulated by Müller et al. exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance (local temperature) of individuals. The effect of external noise is considered here as a second temperature added to the decision of individuals who consider a change of accommodation. A numerical evidence is presented for a discontinuous phase transition of the magnetization.

  9. Quantum critical behavior of the quantum Ising model on fractal lattices

    NASA Astrophysics Data System (ADS)

    Yi, Hangmo

    2015-01-01

    I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.

  10. Relations between short-range and long-range Ising models.

    PubMed

    Angelini, Maria Chiara; Parisi, Giorgio; Ricci-Tersenghi, Federico

    2014-06-01

    We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J∝r{-d-σ}) on both a one-dimensional chain (d=1) and a square lattice (d=2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d=2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one. PMID:25019738

  11. Bootstrapping mixed correlators in the 3D Ising model

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

    We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ2 global symmetry. For the leading ℤ2-odd operator σ and ℤ2-even operator ɛ, we obtain numerical constraints on the allowed dimensions (Δ σ , Δ ɛ ) assuming that σ and ɛ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ σ , Δ ɛ ) space compatible with the known values in the 3D Ising CFT.

  12. Thermodynamic Casimir effect for films in the three-dimensional Ising universality class: Symmetry-breaking boundary conditions

    NASA Astrophysics Data System (ADS)

    Hasenbusch, Martin

    2010-09-01

    We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry-breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++ , where all spins at the boundary are fixed to +1 and +- , where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1 . An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to L0-ω , where L0 is the thickness of the film and ω≈0.8 , can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. The analysis of our data shows that these corrections can be accounted for by an effective thickness L0,eff=L0+Ls . Studying the correlation length of the films, the energy per area, the magnetization profile, and the thermodynamic Casimir force at the bulk critical point we find Ls=1.9(1) for our model and the boundary conditions discussed here. Using this result for Ls we find a nice collapse of the finite-size scaling curves obtained for the thicknesses L0=8.5 , 16.5, and 32.5 for the full range of temperatures that we consider. We compare our results for the finite-size scaling functions θ++ and θ+- of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods, and an experiment with a classical binary liquid mixture.

  13. The Finite-Size Scaling Study of the Ising Model for the Fractals

    NASA Astrophysics Data System (ADS)

    Merdan, Z.; Bayirli, M.; Günen, A.; Bülbül, M.

    2016-04-01

    The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and df^{β } =1.876(8), df^{γ } =3.747(10), df^{α } =2.081(68), df^{δ } =1.940(22), df^{η } =2.178(10), df^{ν } =2.960(22), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and df^{β } =1.875, df^{γ } =3.75, df^{α } =2, df^{δ } =1.933, df^{η } =2.25, df^{ν } =3.

  14. Bond-cluster approximation to the axial next-nearest-neighbor Ising model

    NASA Astrophysics Data System (ADS)

    Taylor, James H.; Desjardins, J. S.

    1984-11-01

    The three-dimensional simple-cubic spin- 1/2 axial next-nearest-neighbor Ising model is studied by means of Kikuchi's cluster-variation method employing a new technique described previously [J. S. Desjardins and O. Steinsvoll,

    [Phys. Scr. 28, 565 (1983)]
    for the solution of the general equations of equilibrium. The particular solution employed in this paper is equivalent to Bethe's first approximation and yields a surprisingly rich phase diagram with modulated structures appearing up to a repeat distance of 15 planes (the highest studied). The phase diagram obtained by our technique resembles closely the mean-field, spin- 1/2 phase diagram of von Boehm and Bak with some significant differences: The second-order boundary of the paramagnetic region is at a significantly lower temperature with a minimum at | κ |˜0.4, where κ is the ratio of the antiferromagnetic to the ferromagnetic coupling constant. In addition, we are able to follow the temperature dependence of the shape of the modulated solutions from the squared-off, low-temperature behavior of Selke and Fisher to the sinusoidal behavior of the high-temperature, mean-field results. The position of our Lifshitz point is in good agreement with previous results, as is the conclusion that transitions between phases are of first order. By contrast, in two dimensions the same approximation completely fails to reproduce reported features of the phase diagram.

  15. Monte Carlo simulation of domain growth in the kinetic Ising model on the connection machine

    NASA Astrophysics Data System (ADS)

    Amar, Jacques G.; Sullivan, Francis

    1989-10-01

    A fast multispin algorithm for the Monte Carlo simulation of the two-dimensional spin-exchange kinetic Ising model, previously described by Sullivan and Mountain and used by Amar et al. has been adapted for use on the Connection Machine and applied as a first test in a calculation of domain growth. Features of the code include: (a) the use of demon bits, (b) the simulation of several runs simultaneously to improve the efficiency of the code, (c) the use of virtual processors to simulate easily and efficiently a larger system size, (d) the use of the (NEWS) grid for last communication between neighbouring processors and updating of boundary layers, (e) the implementation of an efficient random number generator much faster than that provided by Thinking Machines Corp., and (f) the use of the LISP function "funcall" to select which processors to update. Overall speed of the code when run on a (128x128) processor machine is about 130 million attempted spin-exchanges per second, about 9 times faster than the comparable code, using hardware vectorised-logic operations and 64-bit multispin coding on the Cyber 205. The same code can be used on a larger machine (65 536 processors) and should produce speeds in excess of 500 million attempted spin-exchanges per second.

  16. 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.

  17. 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

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

    NASA Astrophysics Data System (ADS)

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-10-01

    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.

  19. Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions

    NASA Astrophysics Data System (ADS)

    Aspelmeier, T.; Wang, Wenlong; Moore, M. A.; Katzgraber, Helmut G.

    2016-08-01

    The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.

  20. Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions.

    PubMed

    Aspelmeier, T; Wang, Wenlong; Moore, M A; Katzgraber, Helmut G

    2016-08-01

    The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems.

  1. Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions.

    PubMed

    Aspelmeier, T; Wang, Wenlong; Moore, M A; Katzgraber, Helmut G

    2016-08-01

    The one-dimensional Ising spin-glass model with power-law long-range interactions is a useful proxy model for studying spin glasses in higher space dimensions and for finding the dimension at which the spin-glass state changes from having broken replica symmetry to that of droplet behavior. To this end we have calculated the exponent that describes the difference in free energy between periodic and antiperiodic boundary conditions. Numerical work is done to support some of the assumptions made in the calculations and to determine the behavior of the interface free-energy exponent of the power law of the interactions. Our numerical results for the interface free-energy exponent are badly affected by finite-size problems. PMID:27627255

  2. Pseudolikelihood decimation algorithm improving the inference of the interaction network in a general class of Ising models.

    PubMed

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2014-02-21

    In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.

  3. Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models

    NASA Astrophysics Data System (ADS)

    Decelle, Aurélien; Ricci-Tersenghi, Federico

    2014-02-01

    In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the ℓ1 regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM.

  4. Universal critical behavior of the two-dimensional Ising spin glass

    NASA Astrophysics Data System (ADS)

    Fernandez, L. A.; Marinari, E.; Martin-Mayor, V.; Parisi, G.; Ruiz-Lorenzo, J. J.

    2016-07-01

    We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

  5. Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides

    NASA Astrophysics Data System (ADS)

    Wu, Jianda; Si, Qimiao; Abrahams, Elihu

    2016-03-01

    Considerations of the observed bad-metal behavior in Fe-based superconductors led to an early proposal for quantum criticality induced by isoelectronic P for As doping in iron arsenides, which has since been experimentally confirmed. We study here an effective model for the isoelectronically tuned pnictides using a large-N approach. The model contains antiferromagnetic and Ising-nematic order parameters appropriate for J1-J2 exchange-coupled local moments on an Fe square lattice, and a damping caused by coupling to itinerant electrons. The zero-temperature magnetic and Ising transitions are concurrent and essentially continuous. The order-parameter jumps are very small, and are further reduced by the interplane coupling; consequently, quantum criticality occurs over a wide dynamical range. Our results reconcile recent seemingly contradictory experimental observations concerning the quantum phase transition in the P-doped iron arsenides.

  6. Non-equilibrium critical properties of the Ising model on product graphs

    NASA Astrophysics Data System (ADS)

    Burioni, Raffaella; Corberi, Federico; Vezzani, Alessandro

    2010-12-01

    We study numerically the non-equilibrium critical properties of the Ising model defined on direct products of graphs, obtained from factor graphs without phase transition (Tc = 0). On this class of product graphs, the Ising model features a finite temperature phase transition, and we find a pattern of scaling behaviors analogous to the one known on regular lattices: observables take a scaling form in terms of a function L(t) of time, with the meaning of a growing length inside which a coherent fractal structure, the critical state, is progressively formed. Computing universal quantities, such as the critical exponents and the limiting fluctuation-dissipation ratio X_\\infty , allows us to comment on the possibility to extend universality concepts to the critical behavior on inhomogeneous substrates.

  7. Influence of Boundary Conditions on Metastable Lifetimes for The Ising Model on the Hyperbolic Plane

    NASA Astrophysics Data System (ADS)

    Richards, Howard L.; Sharma Chapagain, Dipendra; Molchanoff, James

    2012-02-01

    Some corals grow in shapes that resemble 3D models of the hyperbolic plane, since this allows them to have greater area for a given growth radius. Each polyp could be represented by an Ising site, with ``feeding'' = ``up'' and ``retracted'' = ``down''. The mechanisms of metastable decay could be interpreted as how the coral as a whole reacts to changing conditions of food availability or predation. Previous studies have shown that there is a spinodal field for the Ising model on a regular lattice in the hyperbolic plane if it is infinite or has periodic or mean-field boundary conditions. This happens because the size of the boundary grows asymptotically at the same rate as the droplet volume, in clear contrast with droplets in the Euclidean plane. Our simulations show, however, that the spinodal field disappears if more physically relevant open boundary conditions are used instead.

  8. Ising-like phase transition of an n-component Eulerian face-cubic model.

    PubMed

    Ding, Chengxiang; Guo, Wenan; Deng, Youjin

    2013-11-01

    By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph. PMID:24329232

  9. Ising-like phase transition of an n-component Eulerian face-cubic model

    NASA Astrophysics Data System (ADS)

    Ding, Chengxiang; Guo, Wenan; Deng, Youjin

    2013-11-01

    By means of Monte Carlo simulations and a finite-size scaling analysis, we find a critical line of an n-component Eulerian face-cubic model on the square lattice and the simple cubic lattice in the region v>1, where v is the bond weight. The phase transition belongs to the Ising universality class independent of n. The critical properties of the phase transition can also be captured by the percolation of the complement of the Eulerian graph.

  10. Inference of the sparse kinetic Ising model using the decimation method.

    PubMed

    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)] 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 ℓ(1)-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 ℓ(1)-optimization-based methods. PMID:26066148

  11. Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence

    NASA Astrophysics Data System (ADS)

    Foss-Feig, M.; Hazzard, K. R. A.; Bollinger, J. J.; Rey, A. M.; Clark, C. W.

    2013-11-01

    Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t = 0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Foss-Feig et al (2013 Phys. Rev. A 87 042101). Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T1 (spontaneous spin relaxation/excitation) and T2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback.

  12. Evidence for two-dimensional Ising superconductivity in gated MoS₂.

    PubMed

    Lu, J M; Zheliuk, O; Leermakers, I; Yuan, N F Q; Zeitler, U; Law, K T; Ye, J T

    2015-12-11

    The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field. PMID:26563134

  13. Evidence for two-dimensional Ising superconductivity in gated MoS2

    NASA Astrophysics Data System (ADS)

    Lu, J. M.; Zheliuk, O.; Leermakers, I.; Yuan, N. F. Q.; Zeitler, U.; Law, K. T.; Ye, J. T.

    2015-12-01

    The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field Bc2 far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced Bc2 is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

  14. Evidence for two-dimensional Ising superconductivity in gated MoS₂.

    PubMed

    Lu, J M; Zheliuk, O; Leermakers, I; Yuan, N F Q; Zeitler, U; Law, K T; Ye, J T

    2015-12-11

    The Zeeman effect, which is usually detrimental to superconductivity, can be strongly protective when an effective Zeeman field from intrinsic spin-orbit coupling locks the spins of Cooper pairs in a direction orthogonal to an external magnetic field. We performed magnetotransport experiments with ionic-gated molybdenum disulfide transistors, in which gating prepared individual superconducting states with different carrier dopings, and measured an in-plane critical field B(c2) far beyond the Pauli paramagnetic limit, consistent with Zeeman-protected superconductivity. The gating-enhanced B(c2) is more than an order of magnitude larger than it is in the bulk superconducting phases, where the effective Zeeman field is weakened by interlayer coupling. Our study provides experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field.

  15. Phase transition of p-adic Ising λ-model

    SciTech Connect

    Dogan, Mutlay; Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    We consider an interaction of the nearest-neighbors and next nearest-neighbors for the mixed type p-adic λ-model with spin values (−1, +1) on a Cayley tree of order two. In the previous work we have proved the existence of the p-adic Gibbs measure for the model. In this work we have proved the existence of the phase transition occurs for the model.

  16. Ising spin network states for loop quantum gravity: a toy model for phase transitions

    NASA Astrophysics Data System (ADS)

    Feller, Alexandre; Livine, Etera R.

    2016-03-01

    Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should emerge entirely from the correlations between the gravity fluctuations. In the context of loop quantum gravity, quantum states of geometry are defined as spin networks. These are graphs decorated with spin and intertwiners, which represent quantized excitations of areas and volumes of the space geometry. Here, we develop the condensed-matter point of view on extracting the physical and geometrical information from spin network states: we introduce new Ising spin network states, both in 2d on a square lattice and in 3d on a hexagonal lattice, whose correlations map onto the usual Ising model in statistical physics. We construct these states from the basic holonomy operators of loop gravity and derive a set of local Hamiltonian constraints that entirely characterize our states. We discuss their phase diagram and show how the distance can be reconstructed from the correlations in the various phases. Finally, we propose generalizations of these Ising states, which open the perspective to study the coarse-graining and dynamics of spin network states using well-known condensed-matter techniques and results.

  17. Phase transitions and universality in nonequilibrium steady states of stochastic Ising models

    SciTech Connect

    Wang, J.S.; Lebowitz, J.L.

    1988-06-01

    We present results of direct computer simulations and of Monte Carlo renormalization group (MCRG) studies of the nonequilibrium steady states of a spin system with competing dynamics and of the voter model. The MCRG method, previously used only for equilibrium systems, appears to give useful information also for these nonequilibrium systems. The critical exponents are found to be of Ising type for the competing dynamics model at its second-order phase transitions, and of mean-field type for the voter model (consistent with known results for the latter).

  18. 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.

  19. Revisiting 2D Lattice Based Spin Flip-Flop Ising Model: Magnetic Properties of a Thin Film and Its Temperature Dependence

    ERIC Educational Resources Information Center

    Singh, Satya Pal

    2014-01-01

    This paper presents a brief review of Ising's work done in 1925 for one dimensional spin chain with periodic boundary condition. Ising observed that no phase transition occurred at finite temperature in one dimension. He erroneously generalized his views in higher dimensions but that was not true. In 1941 Kramer and Wannier obtained…

  20. Comparison of the dipolar magnetic field generated by two Ising-like models

    NASA Astrophysics Data System (ADS)

    Peqini, Klaudio; Duka, Bejo

    2015-04-01

    We consider two Ising-like models named respectively the "domino" model and the Rikitake disk dynamo model. Both models are based on some collective interactions that can generate a dipolar magnetic field which reproduces the well-known features of the geomagnetic field: the reversals and secular variation (SV). The first model considers the resultant dipolar magnetic field as formed by the superposition of the magnetic fields generated by the dynamo elements called macrospins, while the second one, starting from the two-disk dynamo action, takes in consideration the collective interactions of several disk dynamo elements. We will apply two versions of each model: the short-range and the long-range coupled dynamo elements. We will study the statistical properties of the time series generated by the simulation of all models. The comparison of these results with the paleomagnetic data series and long series of SV enables us to conclude which of these Ising-like models better match with the geomagnetic field time series. Key words: geomagnetic field, domino model, Rikitake disk dynamo, dipolar moment

  1. 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.

  2. Critical wetting in the two-dimensional Ising ferromagnet confined between inhomogeneous walls

    NASA Astrophysics Data System (ADS)

    Trobo, Marta L.; Albano, Ezequiel V.

    2014-12-01

    We present a numerical study of the critical wetting behavior of an Ising magnet confined between two walls, separated by a distance L, where short-range inhomogeneous surface magnetic fields act. So, samples are assumed to have a size L × M, L being the width and M the length, respectively. By considering surface fields varying spatially with a given wavelength or period (λ), H1(x,λ) with 1 ≤ x ≤ M, we found that the wetting temperature is given by the exact result of Abraham [D.B. Abraham, Phys. Rev. Lett. 44, 1165 (1980)] provided that an effective field given by the spacial average[-3.4mm] value (Heff ≡ 1/λ ƒ0 λH1(x,λ)dx > 0) is considered. The above results hold in the low wavelength regime, while for λ → ∞ and a bivaluated surface field (i.e., Hmax for x ≤ M/ 2, and δHmax for x>M/ 2, with 0 <δ< 1), one observes two almost independent wetting transitions, both being compatible with Abraham's exact results corresponding to Hmax and δHmax, respectively. On the other hand, for H1(x,λ) ≠ 0 but Heff = 0 bulk standard critical behavior results is observed.

  3. On the p-spin interaction transverse Ising spin-glass model without replicas

    NASA Astrophysics Data System (ADS)

    De Cesare, L.; Lukierska-Walasek, K.; Rabuffo, I.; Walasek, K.

    1995-02-01

    The p-spin interaction Ising spin glass model in the presence of a transverse field is studied in the large p-limit by means of a convenient operator extension of the cavity fields method avoiding replicas and the Trotter-Suzuki transformation. The results appear quite consistent with those recently obtained for the same model using conventional treatments within the replica trick. This gives additional support to the cavity fields approach as a promising tool towards a general theory of classical and quantum spin glasses.

  4. A threaded Java concurrent implementation of the Monte-Carlo Metropolis Ising model

    PubMed Central

    Castañeda-Marroquín, Carlos; de la Puente, Alfonso Ortega; Alfonseca, Manuel; Glazier, James A.; Swat, Maciej

    2010-01-01

    This paper describes a concurrent Java implementation of the Metropolis Monte-Carlo algorithm that is used in 2D Ising model simulations. The presented method uses threads, monitors, shared variables and high level concurrent constructs that hide the low level details. In our algorithm we assign one thread to handle one spin flip attempt at a time. We use special lattice site selection algorithm to avoid two or more threads working concurently in the region of the lattice that “belongs” to two or more different spins undergoing spin-flip transformation. Our approach does not depend on the current platform and maximizes concurrent use of the available resources. PMID:21814633

  5. Density of zeros of the ferromagnetic Ising model on a family of fractals.

    PubMed

    Knežević, Milan; Knežević, Dragica

    2012-06-01

    We studied distribution of zeros of the partition function of the ferromagnetic Ising model near the Yang-Lee edge on a family of Sierpinski gasket lattices whose members are labeled by an integer b (2 ≤ b<∞). The obtained exact results on the first seven members of this family show that, for b ≥ 4, associated correlation length diverges more slowly than any power law when distance δh from the edge tends to zero, ξ_{YL}∼exp[ln(b)sqrt[|ln(δh)|/ln(λ{0})

  6. Dissipative transverse-field Ising model: Steady-state correlations and spin squeezing

    NASA Astrophysics Data System (ADS)

    Lee, Tony E.; Chan, Ching-Kit

    2013-12-01

    We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, despite the decoherence from spontaneous emission. We analytically calculate fluctuations beyond mean-field theory using a phase-space approach, which involves converting the master equation into a Fokker-Planck equation for the Wigner function. Our calculations are relevant to current experiments with trapped ions.

  7. Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain

    SciTech Connect

    Wang Xiaoting; Schirmer, Sophie G.; Bayat, Abolfazl; Bose, Sougato

    2010-07-15

    We discuss how to prepare an Ising chain in a GHZ state using a single global control field only. This model does not require the spins to be individually addressable and is applicable to quantum systems such as cold atoms in optical lattices, some liquid- or solid-state NMR experiments, and many nanoscale quantum structures. We show that GHZ states can always be reached asymptotically from certain easy-to-prepare initial states using adiabatic passage, and under certain conditions finite-time reachability can be ensured. To provide a reference useful for future experimental implementations, three different control strategies to achieve the objective--adiabatic passage, Lyapunov control, and optimal control--are compared, and their advantages and disadvantages discussed, in particular in the presence of realistic imperfections such as imperfect initial state preparation, system inhomogeneity, and dephasing.

  8. Noncyclic geometric quantum computation and preservation of entanglement for a two-qubit Ising model

    NASA Astrophysics Data System (ADS)

    Rangani Jahromi, H.; Amniat-Talab, M.

    2015-10-01

    After presenting an exact analytical solution of time-dependent Schrödinger equation, we study the dynamics of entanglement for a two-qubit Ising model. One of the spin qubits is driven by a static magnetic field applied in the direction of the Ising interaction, while the other is coupled with a rotating magnetic field. We also investigate how the entanglement can be controlled by changing the external parameters. Because of the important role of maximally entangled Bell states in quantum communication, we focus on the generalized Bell states as the initial states of the system. It is found that the entanglement evolution is independent of the initial Bell states. Moreover, we can preserve the initial maximal entanglement by adjusting the angular frequency of the rotating field or controlling the exchange coupling between spin qubits. Besides, our calculation shows that the entanglement dynamics is unaffected by the static magnetic field imposed in the direction of the Ising interaction. This is an interesting result, because, as we shall show below, this driving field can be used to control and manipulate the noncyclic geometric phase without affecting the system entanglement. Besides, the nonadiabatic and noncyclic geometric phase for evolved states of the present system are calculated and described in detail. In order to identify the unusable states for quantum communication, completely deviated from the initial maximally entangled states, we also study the fidelity between the initial Bell state and the evolved state of the system. Interestingly, we find that these unusable states can be detected by geometric quantum computation.

  9. A mean field Ising model for cortical rotation in amphibian one-cell stage embryos.

    PubMed

    Tuszynski, Jack A; Gordon, Richard

    2012-09-01

    We propose a new physical mechanism of cortical rotation generation in one-cell embryos of amphibians based on a phase transition in the ensemble of microtubules localized to the cortical region of the cell interior. Microtubules, protein polymers formed from tubulin heterodimers, are highly negatively charged, which results in strong electrostatic interactions over tens of nanometers, even in the presence of counterions that partially screen electrostatic interactions. A simplified model that offers a plausible representation of these effects is based on the Ising Hamiltonian, which has been robustly applied to explain a wide range of order-disorder transitions in physics, chemistry and other sciences. An Ising model phase transition, especially with the supercooperative flow alignment effect of global rotation of the cortex, provides an alternative to models of cortical rotation based on microtubule polymerization or motor molecules. Insofar as there is any reality to the concept that microtubules are involved in consciousness, we propose that cortical rotation in the one-cell embryo is a better place to look for the purported microtubule entanglement or coherence properties than the adult brain. PMID:22626532

  10. Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system.

    PubMed

    Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng

    2016-01-01

    The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775

  11. Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system

    NASA Astrophysics Data System (ADS)

    Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng

    2016-03-01

    The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.

  12. Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system

    PubMed Central

    Gong, Ming; Wen, Xueda; Sun, Guozhu; Zhang, Dan-Wei; Lan, Dong; Zhou, Yu; Fan, Yunyi; Liu, Yuhao; Tan, Xinsheng; Yu, Haifeng; Yu, Yang; Zhu, Shi-Liang; Han, Siyuan; Wu, Peiheng

    2016-01-01

    The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena. PMID:26951775

  13. FAST TRACK COMMUNICATION: Variational approach to the scaling function of the 2D Ising model in a magnetic field

    NASA Astrophysics Data System (ADS)

    Mangazeev, Vladimir V.; Batchelor, Murray T.; Bazhanov, Vladimir V.; Dudalev, Michael Yu

    2009-01-01

    The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data are in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general, the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.

  14. Phase transitions and multicritical behavior in the Ising model with dipolar interactions

    NASA Astrophysics Data System (ADS)

    Bab, M. A.; Horowitz, C. M.; Rubio Puzzo, M. L.; Saracco, G. P.

    2016-10-01

    In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (hn) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ . The obtained results indicate that the h1-TL phase transition line is continuous up to δ =1.2585 , while for the h2-TL line a weak first-order character is found in the interval 1.2585 ≤δ ≤1.36 and becomes continuous for 1.37 ≤δ ≤1.9 . This result suggests the existence of a tricritical point close to δ =1.37 . When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h1-h2 line, i.e., at δ =1.2585 , the critical phase corresponding to the h1-TL transition coexists with the h2 phase.

  15. Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer

    PubMed Central

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

    2014-01-01

    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. PMID:25029660

  16. Ising-nematic order in the bilinear-biquadratic model for the iron pnictides

    NASA Astrophysics Data System (ADS)

    Bilbao Ergueta, Patricia; Nevidomskyy, Andriy H.

    2015-10-01

    Motivated by the recent inelastic neutron scattering (INS) measurements in the iron pnictides which show a strong anisotropy of spin excitations even above the magnetic transition temperature TN, we study the spin dynamics within the frustrated Heisenberg model with biquadratic spin-spin exchange interactions. Using the Dyson-Maleev (DM) representation, which proves appropriate for all temperature regimes, we find that the spin-spin dynamical structure factors are in excellent agreement with experiment, exhibiting breaking of the C4 symmetry even into the paramagnetic region TNIsing-nematic phase. In addition to the Heisenberg spin interaction, we include the biquadratic coupling -K (Si.Sj) 2 and study its effect on the dynamical temperature range Tσ-TN of the Ising-nematic phase. We find that this range reduces dramatically when even small values of the interlayer exchange Jc and biquadratic coupling K are included. To supplement our analysis, we benchmark the results obtained using full decoupling in the DM method against those from different nonlinear spin-wave theories, including the recently developed generalized spin-wave theory (GSWT), and find good qualitative agreement among the different theoretical approaches as well as experiment for both the spin-wave dispersions and the dynamical structure factors.

  17. Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction

    NASA Astrophysics Data System (ADS)

    Wang, Qiong; He, Zhi; Yao, Chun-Mei

    2015-04-01

    We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46 (2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated. Supported by the National Natural Science Foundation of China under Grant Nos. 61475045 and 11347142, the Natural Science Foundation of Hunan Province, China under Grant No. 2015JJ3092

  18. Self-organizing Ising model of artificial financial markets with small-world network topology

    NASA Astrophysics Data System (ADS)

    Zhao, Haijie; Zhou, Jie; Zhang, Anghui; Su, Guifeng; Zhang, Yi

    2013-01-01

    We study a self-organizing Ising-like model of artificial financial markets with underlying small-world (SW) network topology. The asset price dynamics results from the collective decisions of interacting agents which are located on a small-world complex network (the nodes symbolize the agents of a financial market). The model incorporates the effects of imitation, the impact of external news and private information. We also investigate the influence of different network topologies, from regular lattice to random graph, on the asset price dynamics by adjusting the probability of the rewiring procedure. We find that a specific combination of model parameters reproduce main stylized facts of real-world financial markets.

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

    SciTech Connect

    Kriz, Igor; Loebl, Martin; Somberg, Petr

    2013-05-15

    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.

  20. Effective time reversal and echo dynamics in the transverse field Ising model

    NASA Astrophysics Data System (ADS)

    Schmitt, Markus; Kehrein, Stefan

    2016-09-01

    The question of thermalisation in closed quantum many-body systems has received a lot of attention in the past few years. An intimately related question is whether a closed quantum system shows irreversible dynamics. However, irreversibility and what we actually mean by this in a quantum many-body system with unitary dynamics has been explored very little. In this work we investigate the dynamics of the Ising model in a transverse magnetic field involving an imperfect effective time reversal. We propose a definition of irreversibility based on the echo peak decay of observables. Inducing the effective time reversal by different protocols we find an algebraic decay of the echo peak heights or an ever persisting echo peak indicating that the dynamics in this model is well reversible.

  1. The Ising Model on Pure Husimi Lattices: A General Formulation and the Critical Temperatures

    NASA Astrophysics Data System (ADS)

    Jurčišinová, E.; Jurčišin, M.

    2012-07-01

    We consider the Ising spin 1/2 model on arbitrary pure Husimi lattices. An effective representation for the recursion relations is found which allows to write the general solution of the model in an fluent unified way for all pure Husimi lattices. In this respect, explicit expressions for the spontaneous magnetization, for the susceptibility, for the free energy, and for the specific heat are found. Besides, it is shown that this representation allows also to determine exactly the position of the critical temperature on arbitrary pure Husimi lattice. It is found that the critical temperatures for all pure Husimi lattices are driven by a single polynomial equation with coefficients given by parameters that uniquely describe the lattices.

  2. Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number

    NASA Astrophysics Data System (ADS)

    Shukla, Prabodh; Thongjaomayum, Diana

    2016-06-01

    We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1-c have z = 3. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of c\\gt 0. This extends earlier results for c = 0 and c = 1 to the entire range 0≤slant c≤slant 1, and provides new insight in non-equilibrium critical phenomena. Our analysis shows that a spanning avalanche can occur on a lattice even in the absence of a spanning cluster of z = 4 sites.

  3. Order by disorder in the antiferromagnetic Ising model on an elastic triangular lattice

    PubMed Central

    Shokef, Yair; Souslov, Anton; Lubensky, T. C.

    2011-01-01

    Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher-order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order by disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level and, contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state. PMID:21730164

  4. Almost Gibbsianness and Parsimonious Description of the Decimated 2d-Ising Model

    NASA Astrophysics Data System (ADS)

    Le Ny, Arnaud

    2013-07-01

    In this paper, we complete and provide details for the existing characterizations of the decimation of the Ising model on {Z}2 in the generalized Gibbs context. We first recall a few features of the Dobrushin program of restoration of Gibbsianness and present the construction of global specifications consistent with the extremal decimated measures. We use them to prove that these renormalized measures are almost Gibbsian at any temperature and to analyse in detail its convex set of DLR measures. We also recall the weakly Gibbsian description and complete it using a potential that admits a quenched correlation decay, i.e. a well-defined configuration-dependent length beyond which this potential decays exponentially. We use these results to incorporate these decimated measures in the new framework of parsimonious random fields that has been recently developed to investigate probability aspects related to neurosciences.

  5. Effective-field theory on the kinetic spin-3/2 Ising model

    NASA Astrophysics Data System (ADS)

    Shi, Xiaoling; Qi, Yang

    2015-11-01

    The effective-field theory (EFT) is used to study the dynamical response of the kinetic spin-3/2 Ising model in the presence of a sinusoidal oscillating magnetic field. The effective-field dynamic equations are given for the honeycomb lattices (Z = 3). The dynamic order parameter, the dynamic quadrupole moment are calculated. We have found that the behavior of the system strongly depends on the crystal field interaction D. The dynamic phase boundaries are obtained, and there is no dynamic tricritical point on the dynamic phase transition line. The results are also compared with previous results which obtained from the mean-field theory (MFT) and the effective-field theory (EFT) for the square lattices (Z = 4). Different dynamic phase transition lines show that the thermal fluctuations are a key factor of the dynamic phase transition.

  6. The cellular Ising model: a framework for phase transitions in multicellular environments.

    PubMed

    Weber, Marc; Buceta, Javier

    2016-06-01

    Inspired by the Ising model, we introduce a gene regulatory network that induces a phase transition that coordinates robustly the behaviour of cell ensembles. The building blocks of the design are the so-called toggle switch interfaced with two quorum sensing modules, Las and Lux. We show that as a function of the transport rate of signalling molecules across the cell membrane the population undergoes a spontaneous symmetry breaking from cells individually switching their phenotypes to a global collective phenotypic organization. By characterizing the critical behaviour, we reveal some properties, such as phenotypic memory and hypersensitivity, with relevance in the field of synthetic biology. We argue that our results can be extrapolated to other multicellular systems and be a generic framework for collective decision-making processes. PMID:27307510

  7. Long-range random transverse-field Ising model in three dimensions

    NASA Astrophysics Data System (ADS)

    Kovács, István A.; Juhász, Róbert; Iglói, Ferenc

    2016-05-01

    We consider the random transverse-field Ising model in d =3 dimensions with long-range ferromagnetic interactions which decay as a power α >d with the distance. Using a variant of the strong-disorder renormalization group method we study numerically the phase-transition point from the paramagnetic side. We find that the fixed point controlling the transition is of the strong-disorder type, and based on experience with other similar systems, we expect the results to be qualitatively correct, but probably not asymptotically exact. The distribution of the (sample dependent) pseudocritical points is found to scale with 1 /lnL , L being the linear size of the sample. Similarly, the critical magnetization scales with (lnL) χ/Ld and the excitation energy behaves as L-α. Using extreme-value statistics we argue that extrapolating from the ferromagnetic side the magnetization approaches a finite limiting value and thus the transition is of mixed order.

  8. Quantum phase transition of the transverse-field quantum Ising model on scale-free networks.

    PubMed

    Yi, Hangmo

    2015-01-01

    I investigate the quantum phase transition of the transverse-field quantum Ising model in which nearest neighbors are defined according to the connectivity of scale-free networks. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and study its scaling characteristics. For the degree exponent λ=6, I obtain results that are consistent with the mean-field theory. For λ=4.5 and 4, however, the results suggest that the quantum critical point belongs to a non-mean-field universality class. Further simulations indicate that the quantum critical point remains mean-field-like if λ>5, but it continuously deviates from the mean-field theory as λ becomes smaller.

  9. Complexity in mean-field spin-glass models: Ising p-spin

    SciTech Connect

    Crisanti, A.; Leuzzi, L.; Rizzo, T.

    2005-03-01

    The complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising p-spin is investigated in the temperature regime where the equilibrium phase is one-step replica symmetry breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution, the latter accounting for the total number of solutions. The relevant TAP solutions counted by the non-SUSY complexity share the same features of the corresponding solutions in the Sherrington-Kirkpatrick model; in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY complexity, instead, are well separated minima.

  10. Highly optimized simulations on single- and multi-GPU systems of the 3D Ising spin glass model

    NASA Astrophysics Data System (ADS)

    Lulli, M.; Bernaschi, M.; Parisi, G.

    2015-11-01

    We present a highly optimized implementation of a Monte Carlo (MC) simulator for the three-dimensional Ising spin-glass model with bimodal disorder, i.e., the 3D Edwards-Anderson model running on CUDA enabled GPUs. Multi-GPU systems exchange data by means of the Message Passing Interface (MPI). The chosen MC dynamics is the classic Metropolis one, which is purely dissipative, since the aim was the study of the critical off-equilibrium relaxation of the system. We focused on the following issues: (i) the implementation of efficient memory access patterns for nearest neighbours in a cubic stencil and for lagged-Fibonacci-like pseudo-Random Numbers Generators (PRNGs); (ii) a novel implementation of the asynchronous multispin-coding Metropolis MC step allowing to store one spin per bit and (iii) a multi-GPU version based on a combination of MPI and CUDA streams. Cubic stencils and PRNGs are two subjects of very general interest because of their widespread use in many simulation codes.

  11. Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins.

    PubMed

    Britton, Joseph W; Sawyer, Brian C; Keith, Adam C; Wang, C-C Joseph; Freericks, James K; Uys, Hermann; Biercuk, Michael J; Bollinger, John J

    2012-04-26

    The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J(i,j), on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,j) is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism

  12. Convex-set description of quantum phase transitions in the transverse Ising model using reduced-density-matrix theory.

    PubMed

    Schwerdtfeger, Christine A; Mazziotti, David A

    2009-06-14

    Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter controlling the phase transition [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 74, 012501 (2006)]. For the one-dimensional transverse Ising model quantum phase transitions as well as their finite-lattice analogs are computed and characterized by the 2-RDM movement with respect to the transverse magnetic field strength g. The definition of a 2-RDM "speed" quantifies the movement of the 2-RDM per unit of g, which reaches its maximum at the critical point of the phase transition. For the infinite lattice the convex set of 2-RDMs and the 2-RDM speed are computed from the exact solution of the 2-RDM in the thermodynamic limit of infinite N [P. Pfeuty, Ann. Phys. 57, 79 (1970)]. For the finite lattices we compute the 2-RDM convex set and its speed by the variational 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] in which approximate ground-state 2-RDMs are calculated without N-particle wave functions by using constraints, known as N-representability conditions, to restrict the 2-RDMs to represent quantum system of N fermions. Advantages of the method include: (i) rigorous lower bounds on the ground-state energies, (ii) polynomial scaling of the calculation with N, and (iii) independence of the N-representability conditions from a reference wave function, which enables the modeling of multiple quantum phases. Comparing the 2-RDM convex sets for the finite- and infinite-site lattices reveals that the variational 2-RDM method accurately captures the shape of the convex set and the signature of the phase transition in the 2-RDM movement. From the 2-RDM all one- and two-particle expectation values (or order parameters) of the quantum Ising model can also be computed including the pair correlation function, which

  13. 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.

  14. Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain.

    PubMed

    Ananikian, N S; Ananikyan, L N; Chakhmakhchyan, L A; Rojas, Onofre

    2012-06-27

    The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.

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

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  16. Ising Models, Universality and the Non Renormalization of the Quantum Anomalies

    NASA Astrophysics Data System (ADS)

    Mastropietro, Vieri

    2010-03-01

    A number of universal relations (proposed by Kadanoff, Luther, Peschel and Haldane) are believed to be true in a wide class of systems with continuously varying indices, among which are interacting planar Ising models, vertex or Ashkin-Teller models, quantum spin chains and 1D Fermi systems; by such relations one can predict several quantities in terms of a few measurable parameters without relying on the specific microscopic details. The validity of such relations can be checked in special solvable models but, despite several attempts, the proof of their general validity was up to now an open problem. A rigorous derivation of several of such relations (for solvable and not solvable models and without any use of exact solutions) has been recently obtained in [8] and [11] through Renormalization Group methods. The proof is based on the representation in terms of Grassmann integrals and the validity of the Adler-Bardeen property of the non renormalization of the quantum anomalies in the asymptotic Ward identities. Gauge invariance is exact only in the scaling limit but the lattice corrections can be rigorously taken into account.

  17. Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs

    NASA Astrophysics Data System (ADS)

    Yoon, S.; Goltsev, A. V.; Dorogovtsev, S. N.; Mendes, J. F. F.

    2011-10-01

    We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are treelike (hypertrees), which crucially simplifies the problem and allows us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model with pairwise interactions on the resulting random networks and obtain an exact solution of this model. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary treelike complex networks. However, weak clustering does not change the critical behavior qualitatively. Our solution also gives the birth point of the giant connected component in these loopy networks.

  18. Hidden rotational symmetry in a generalized Ising model with rectangular symmetry

    NASA Astrophysics Data System (ADS)

    Deng, Hai-Yao; Hu, Kaige

    2011-08-01

    Novel quantum phases are of interest both fundamentally and practically. In this paper, a toy lattice model with exact four-fold rotational symmetry (C4), which can be taken as a straightforward generalization of the usual Ising model, is studied. The phase diagram in the t-T plane is plotted, where t is the energy controlling quantum fluctuations and T is the temperature. The diagram features an exotic phase (termed the S-phase), which meets the conventional ordered and disordered phases at a tri-critical point. The S-phase distinguishes itself from the conventional ordered phase by its symmetry properties. In fact, it is shown to arise from the spontaneous breaking of the continuous rotational symmetry rather than the C4 symmetry. This is manifested in the long-wavelength fluctuations, which are shown to be the gapless Nambu-Goldstone modes following a quadratic dispersion relation, similar to that of the XY model. Further, discontinuous quantum phase transitions are found and they are argued to occur subsequent to the S-phase.

  19. Information transfer and criticality in the Ising model on the human connectome.

    PubMed

    Marinazzo, Daniele; Pellicoro, Mario; Wu, Guorong; Angelini, Leonardo; Cortés, Jesús M; Stramaglia, Sebastiano

    2014-01-01

    We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.

  20. 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

  1. Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures

    NASA Astrophysics Data System (ADS)

    Abeling, Nils; Kehrein, Stefan

    The recently discovered Dynamical Phase Transition denotes non-analytic behavior in the real time evolution of quantum systems in the thermodynamic limit and has been shown to occur in different systems at zero temperature [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. In this talk we present the extension of the analysis to non-zero temperature by studying a generalized form of the Loschmidt echo, the work distribution function, of a quantum quench in the transverse field Ising model. Although the quantitative behavior at non-zero temperatures still displays features derived from the zero temperature non-analyticities, it is shown that in this model dynamical phase transitions do not exist if T > 0 . This is a consequence of the system being initialized in a thermal state. Moreover, we elucidate how the Tasaki-Crooks-Jarzynski relation can be exploited as a symmetry relation for a global quench or to obtain the change of the equilibrium free energy density. This work was supported through CRC SFB 1073 (Project B03) of the Deutsche Forschungsgemeinschaft (DFG).

  2. Quantum correlated cluster mean-field theory applied to the transverse Ising model

    NASA Astrophysics Data System (ADS)

    Zimmer, F. M.; Schmidt, M.; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

  3. Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents

    NASA Astrophysics Data System (ADS)

    Mullick, Pratik; Sen, Parongama

    2016-05-01

    We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0 ≤x ≤1 . In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for x ≤0.5 , persistence for the up (minority) spins shows the behavior Pmin(t ) ˜t-γexp[-(t/τ ) δ] with time t , while for the down (majority) spins, Pmaj(t ) approaches a finite value. We find that the timescale τ diverges as (xc-x ) -λ, where xc=0.5 and λ ≃2.31 . The exponent γ varies as θ2 d+c0(xc-x ) β where θ2 d≃0.215 is very close to the persistence exponent in two dimensions; β ≃1 . The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E (x ) =f [(x/-xc xc) L1 /ν] , with ν ≈1.47 . This result suggests that τ ˜Lz ˜ , where z ˜=λ/ν =1.57 ±0.11 is an exponent not explored earlier.

  4. Exact Enumeration of the Phase Space of an Ising Model of Ni2MnGa

    SciTech Connect

    Eisenbach, Markus; Brown, Greg; Rusanu, Aurelian; Odbadrakh, Khorgolkhuu; Nicholson, Don M; McCarthy, Carrie V.

    2013-01-01

    Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the number of degrees of freedom. For an Ising model with sites the number of possible states is requiring the use of better scaling methods such as importance sampling Monte-Carlo calculations for all but the smallest systems. Yet the ability to obtain exact solutions for as large as possible systems can provide important benchmark results and opportunities for unobscured insight into the underlying physicsofthesystem.HerewepresentanIsingmodelforthemagneticsublatticesoftheimportantmagneto-caloricmaterialNi MnGa and use an exact enumeration algorithm to calculate the number of states for each energy and sublattice magne- tizations and . This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing the jaguarpf system at Oak Ridge we are able to calculate for systems of up to48sites,whichprovidesimportantinsightintothemechanismforthelargemagnet-caloriceffectinNi MnGaaswellasanimportant benchmark for Monte-Carlo (esp. Wang-Landau method).

  5. Spot size variation FCS in simulations of the 2D Ising model

    NASA Astrophysics Data System (ADS)

    Burns, Margaret C.; Nouri, Mariam; Veatch, Sarah L.

    2016-06-01

    Spot variation fluorescence correlation spectroscopy (svFCS) was developed to study the movement and organization of single molecules in plasma membranes. This experimental technique varies the size of an illumination area while measuring correlations in time using standard fluorescence correlation methods. Frequently, this data is interpreted using the assumption that correlation measurements reflect the dynamics of single molecule motions, and not motions of the average composition. Here, we explore how svFCS measurements report on the dynamics of components diffusing within simulations of a 2D Ising model with a conserved order parameter. Simulated correlation functions report on both the fast dynamics of single component mobility and the slower dynamics of the average composition. Over a range of simulation conditions, a conventional svFCS analysis suggests the presence of anomalous diffusion even though single molecule motions are nearly Brownian in these simulations. This misinterpretation is most significant when the surface density of the fluorescent label is elevated, therefore we suggest future measurements be made over a range of tracer densities. Some simulation conditions reproduce qualitative features of published svFCS experimental data. Overall, this work emphasizes the need to probe membranes using multiple complimentary experimental methodologies in order to draw conclusions regarding the nature of spatial and dynamical heterogeneity in these systems.

  6. Hysteresis in DNA compaction by Dps is described by an Ising model.

    PubMed

    Vtyurina, Natalia N; Dulin, David; Docter, Margreet W; Meyer, Anne S; Dekker, Nynke H; Abbondanzieri, Elio A

    2016-05-01

    In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps-DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps-DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states.

  7. Quantum correlated cluster mean-field theory applied to the transverse Ising model.

    PubMed

    Zimmer, F M; Schmidt, M; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

  8. Spinodals of the Ising model on the order-4 pentagonal tiling of the hyperbolic plane

    NASA Astrophysics Data System (ADS)

    Richards, Howard L.

    In the Euclidean plane, the Ising model on a regular lattice does not have a true spinodal - that is, there is no local minimum of the free energy that persists forever (in the limit of infinitely large systems) except for the global minimum, which characterizes the stable state. However, a local minimum can persist for a very long time, so the minimum can be referred to as a ``metastable'' state. The manner in which the metastable state decays depends on the strength of the magnetic field and the system size; the ``thermodynamic spinodal'' is the transition between systems large enough to contain a single critical droplet and systems that are too small to do so, and the ``dynamic spinodal'' marks the transition between decay as a Poisson process to decay that is ``deterministic'', meaning the standard deviation of the lifetime of the metastable state is small compared with its mean value. However, in the hyperbolic plane, true metastability exists, and evidence shows that the thermodynamic spinodal and dynamic spinodal are numerically close to the true spinodal, the field below which the metastable state cannot decay through the nucleation and growth of droplets. This research was supported by NSF Grant OCI-1005117.

  9. Quantum correlated cluster mean-field theory applied to the transverse Ising model.

    PubMed

    Zimmer, F M; Schmidt, M; Maziero, Jonas

    2016-06-01

    Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations. PMID:27415217

  10. Influence of nonuniform surface magnetic fields in wetting transitions in a confined two-dimensional Ising ferromagnet

    NASA Astrophysics Data System (ADS)

    Trobo, Marta L.; Albano, Ezequiel V.

    2013-11-01

    Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls where competitive surface fields act. In our finite samples of size L×M, the walls are separated by a distance L, M being the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the form H1,δH1,H1,δH1,..., where the parameter -1≤δ≤1 allows us to control the nonuniformity of the fields. By performing Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of an interface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, such an interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transition that takes place in the thermodynamic limit. By exactly working out the ground state (T=0), we found that besides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for δ<-1/3 and large fields (H1>3), H1tr/J=3, δtr=-1/3,T=0, being a triple point where three phases coexist. By means of Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures; e.g., we examined in detail the case T=0.7×Tcb. Furthermore, we also recorded phase diagrams for fixed values of δ, i.e., plots of the critical field at the wetting transition (H1w) versus T showing, on the one hand, that the exact results of Abraham [Abraham, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.44.1165 44, 1165 (1980)] for δ=1 are recovered, and on the other hand, that extrapolations to T→0 are consistent with our exact results. Based on our numerical results we conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the case of nonuniform fields. In fact, by considering a nonuniform surface field of some period λ, with λ≪M, e.g., [H1(x,λ)>0], one can obtain the effective field Heff at a λ coarse-grained level

  11. Influence of nonuniform surface magnetic fields in wetting transitions in a confined two-dimensional Ising ferromagnet.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V

    2013-11-01

    Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls where competitive surface fields act. In our finite samples of size L×M, the walls are separated by a distance L, M being the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the form H(1),δH(1),H(1),δH(1),..., where the parameter -1≤δ≤1 allows us to control the nonuniformity of the fields. By performing Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of an interface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, such an interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transition that takes place in the thermodynamic limit. By exactly working out the ground state (T=0), we found that besides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for δ<-1/3 and large fields (H(1)>3), H(1)(tr)/J=3, δ(tr)=-1/3,T=0, being a triple point where three phases coexist. By means of Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures; e.g., we examined in detail the case T=0.7×T(cb). Furthermore, we also recorded phase diagrams for fixed values of δ, i.e., plots of the critical field at the wetting transition (H(1w)) versus T showing, on the one hand, that the exact results of Abraham [Abraham, Phys. Rev. Lett. 44, 1165 (1980)] for δ=1 are recovered, and on the other hand, that extrapolations to T→0 are consistent with our exact results. Based on our numerical results we conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the case of nonuniform fields. In fact, by considering a nonuniform surface field of some period λ, with λ0], one can obtain the effective field H(eff) at a λ coarse-grained level given by H(eff)=1/

  12. Degenerate Ising model for atomistic simulation of crystal-melt interfaces.

    PubMed

    Schebarchov, D; Schulze, T P; Hendy, S C

    2014-02-21

    One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level. PMID:24559357

  13. Degenerate Ising model for atomistic simulation of crystal-melt interfaces

    SciTech Connect

    Schebarchov, D.; Schulze, T. P.; Hendy, S. C.

    2014-02-21

    One of the simplest microscopic models for a thermally driven first-order phase transition is an Ising-type lattice system with nearest-neighbour interactions, an external field, and a degeneracy parameter. The underlying lattice and the interaction coupling constant control the anisotropic energy of the phase boundary, the field strength represents the bulk latent heat, and the degeneracy quantifies the difference in communal entropy between the two phases. We simulate the (stochastic) evolution of this minimal model by applying rejection-free canonical and microcanonical Monte Carlo algorithms, and we obtain caloric curves and heat capacity plots for square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions. Since the model admits precise adjustment of bulk latent heat and communal entropy, neither of which affect the interface properties, we are able to tune the crystal nucleation barriers at a fixed degree of undercooling and verify a dimension-dependent scaling expected from classical nucleation theory. We also analyse the equilibrium crystal-melt coexistence in the microcanonical ensemble, where we detect negative heat capacities and find that this phenomenon is more pronounced when the interface is the dominant contributor to the total entropy. The negative branch of the heat capacity appears smooth only when the equilibrium interface-area-to-volume ratio is not constant but varies smoothly with the excitation energy. Finally, we simulate microcanonical crystal nucleation and subsequent relaxation to an equilibrium Wulff shape, demonstrating the model's utility in tracking crystal-melt interfaces at the atomistic level.

  14. A Renormalization Group Study of the Ising Model on the Hierarchical Hanoi Networks

    NASA Astrophysics Data System (ADS)

    Brunson, Clifton Trent

    Despite all the remarkable breakthroughs in the area of complex networks over the last two decades, there still lacks a complete and general understanding of effects that occur when long-range connections are present in a system. This thesis explores the Ising model using recursive hierarchical networks called Hanoi networks (HN) as a substrate. Hanoi networks are purely synthetic and are not found in nature, so it is important to establish and not lose sight of why they worth studying. In essence, we are not strictly interested in HNs themselves, but the generalized statements about phase transitions on complex networks that they provide via the renormalization group (RG). The RG framework on HNs is established in this study and the thermodynamic observables for statistical models are derived from it. Traditionally, the RG has given physicists insight into the critical exponents of a system or model, which leads to universal behavior; however, hyperbolic networks, like the ones currently under investigation, do not contain constant exponents and do not exhibit universality. Instead, it is found that the scaling exponents are functions of the temperature. We ultimately want to answer the questions: What is it about long-range connections that create a break in universal behavior and can complex networks be designed to produce predicted and intended effects in phase behavior? The current state of research is several years or perhaps decades away from fully comprehending the answers to these questions. The research presented here is motivated by these questions, and our contribution here is intended to show a generalized picture of phase transitions on networks.

  15. Finite-size effects for anisotropic 2D Ising model with various boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh

    2012-12-01

    We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

  16. Note: Evidence against 2D-Ising criticality in aqueous solutions with added salt

    NASA Astrophysics Data System (ADS)

    Troncoso, Jacobo; Cerdeiriña, Claudio A.

    2013-11-01

    Coexistence-curve data in the refractive index-temperature plane for solutions of 3-methyl-pyridine in heavy water with a small amount of added sodium tetraphenylborate have been determined. The analysis of such data indicates that this system belongs to the universality class of the three-dimensional Ising model (3D-Ising). This finding contrasts with previous work by Sadakane et al. [Soft Matter 7, 1334 (2011)] in which 2D-Ising criticality is invoked, but agrees with the recent assessment by Leys et al. [Soft Matter 9, 9326 (2013)].

  17. 24-th Order high temperature expansion for the 3-d Ising model

    SciTech Connect

    Glaessner, U.; Schilling, K.; Bhanot, G.; Creutz, M.

    1994-12-01

    The authors present the series for the free energy and their estimate for the critical exponent {alpha}, as computed by a recursive bookkeeping algorithm on the CM5. They begin with a discussion of the algorithm to compute the High-Temperature expansion on finite 3-D Ising lattices.

  18. Adaptive multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model

    NASA Astrophysics Data System (ADS)

    Navarro, Cristóbal A.; Huang, Wei; Deng, Youjin

    2016-08-01

    This work presents an adaptive multi-GPU Exchange Monte Carlo approach for the simulation of the 3D Random Field Ising Model (RFIM). The design is based on a two-level parallelization. The first level, spin-level parallelism, maps the parallel computation as optimal 3D thread-blocks that simulate blocks of spins in shared memory with minimal halo surface, assuming a constant block volume. The second level, replica-level parallelism, uses multi-GPU computation to handle the simulation of an ensemble of replicas. CUDA's concurrent kernel execution feature is used in order to fill the occupancy of each GPU with many replicas, providing a performance boost that is more notorious at the smallest values of L. In addition to the two-level parallel design, the work proposes an adaptive multi-GPU approach that dynamically builds a proper temperature set free of exchange bottlenecks. The strategy is based on mid-point insertions at the temperature gaps where the exchange rate is most compromised. The extra work generated by the insertions is balanced across the GPUs independently of where the mid-point insertions were performed. Performance results show that spin-level performance is approximately two orders of magnitude faster than a single-core CPU version and one order of magnitude faster than a parallel multi-core CPU version running on 16-cores. Multi-GPU performance is highly convenient under a weak scaling setting, reaching up to 99 % efficiency as long as the number of GPUs and L increase together. The combination of the adaptive approach with the parallel multi-GPU design has extended our possibilities of simulation to sizes of L = 32 , 64 for a workstation with two GPUs. Sizes beyond L = 64 can eventually be studied using larger multi-GPU systems.

  19. Some aspects of the chiral Potts model and the Ising model

    NASA Astrophysics Data System (ADS)

    Jin, Bai-Qi

    Scope and method of study. In this thesis, we study two-dimensional statistical physics models. In the first three chapters, the 3-state chiral Potts model is used to study the question of the existence of a Lifshitz point and its related phase transitions. After an introduction in Chapter 1, the mean-field transfer matrix method with effective field determined by Bogoliubov's variational inequality is used to explore the phase diagram of this model in Chapter 2. In Chapter 3, we study this problem by the mean-field transfer matrix method with Weiss- and Bethe-type mean-field approximations respectively, and analyze the nature of the phase transition with the coherent anomaly method. Chapters 4 and 5 are contributions to the study of the Z-invariant Icing model and the quasi periodic Icing model. In Chapter 6, functional relations are used for the calculation of the exact free energy of the integrable chiral Potts model. Findings and conclusions. Our numerical studies indicate that possibly no Lifshitz point exists at finite chirality in the 3-state chiral Potts model. This result is in contrast with many other numerical studies. Furthermore, the coherent anomaly behaviors are examined in these mean-field transfer matrix approximations. Although the coherent anomaly method does give some interesting indications, we find that either much larger systems or some exact information are necessary for us to make a definite conclusion about the nature of the phase transitions in this model. In Chapter 4, the scaling form of the correlation function in the inhomogeneous Z-invariant Icing model is presented and it is applied to the study of quasi-periodic Icing models in Chapter 5. The results provide evidence that the ferromagnetic quasi-periodic Icing model with different strengths of interactions is not much different from the regular Icing model but significantly different---in its wavevector-dependent susceptibility pattern---from the case with both ferro- and

  20. Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field

    DOE PAGES

    Fritsch, Katharina; Ehlers, G.; Rule, K. C.; Habicht, Klaus; Ramazanoglu, Mehmet K.; Dabkowska, H. A.; Gaulin, Bruce D.

    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, Co3V2O8, 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 μ0Hc1~6.25 T and μ0Hc2~7 T is discontinuous, while the final quantum critical point at μ0Hc3~13 T ismore » continuous.« less

  1. Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field

    NASA Astrophysics Data System (ADS)

    Fritsch, K.; Ehlers, G.; Rule, K. C.; Habicht, K.; Ramazanoglu, M.; Dabkowska, H. A.; Gaulin, B. D.

    2015-11-01

    The application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional kagome staircase magnet, Co3V2O8 , 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. At least one of the transitions to incommensurate phases at μ0Hc 1˜6.25 T and μ0Hc 2˜7 T is discontinuous, while the final quantum critical point at μ0Hc 3˜13 T is continuous.

  2. 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.

  3. Magnetic Order in the Frustrated Ising Quasi-One Dimensional Compound NaCo(acac)3 • Benzene

    NASA Astrophysics Data System (ADS)

    Karaki, Yoshitomo; Kuga, Kentaro; Kimura, Kenta; Nakatsuji, Satoru; Matsubayashi, Kazuyuki; Uwatoko, Yoshiya

    2015-08-01

    We report the results of susceptibility, magnetization curve, and specific heat measurements on single crystals of NaCo(acac)3 • benzene, which forms a triangular lattice on the ab-plane with Ising ferromagnetic chains along the c-axis. We found a long-range order below 62 mK by specific heat measurement, a steplike increase in susceptibility at this temperature, and a plateau of one-third of the full moment in the M-H curve at 20 mK. We also observed a spin relaxation that obeys the Arrhenius law in the ordered state. The existence of a partially disordered antiferromagnetic state is discussed on the basis of the results.

  4. XY ring exchange model with frustrated Ising coupling on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Owerre, S. A.

    2016-07-01

    We investigate the nature of a Z2-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. Within the limits of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the Z2-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near k = 0 and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic dispersion near k = 0 in the U(1)-invariant counterpart. We also study the effects of frustration when competing with a classically frustrated Ising interaction. We provide a glimpse into the possible quantum phases that could emerge. A comprehensive understanding of this Hamiltonian, however, cannot be elucidated analytically and requires an explicit numerical simulation.

  5. Magnetic properties of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire

    SciTech Connect

    Kocakaplan, Y.; Ertaş, M.

    2015-10-15

    Magnetic properties, such as magnetizations, internal energy, specific heat, entropy, Helmholtz free energy, and phase diagrams of the spin-3/2 Blume-Capel model on a hexagonal Ising nanowire with core-shell structure are studied by using the effective-field theory with correlations. The hysteresis behaviors of the system are also investigated and the effects of Hamiltonian parameters on hysteresis behaviors are discussed in detail. The obtained results are compared with some theoretical results and a qualitatively good agreement is found.

  6. Performance of Replica-Exchange Wang-Landau Sampling for the 2D Ising Model: A Brief Survey

    SciTech Connect

    Zhao, Yiwei; Cheung, Siu Wun; Li, Ying Wai; Eisenbach, Markus

    2014-01-01

    We report a brief performance study of the replica-exchange Wang-Landau algorithm, a recently proposed parallel realization of Wang-Landau sampling, using the 2D Ising model as a test case. The simulation time is found to scale inversely with the square root of the number of subwindows (and thus number of processors) used to span the global parameter space. We also investigate the time profiles for random walkers in dierent subwindows to complete iterations, which will aid the development of and adaptive load-balancing scheme.

  7. Thermalization, Error Correction, and Memory Lifetime for Ising Anyon Systems

    NASA Astrophysics Data System (ADS)

    Brell, Courtney G.; Burton, Simon; Dauphinais, Guillaume; Flammia, Steven T.; Poulin, David

    2014-07-01

    We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range from 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.

  8. Loss of Ergodicity in the Transition from Annealed to Quenched Disorder in a Finite Kinetic Ising Model

    NASA Astrophysics Data System (ADS)

    Pigeard de Almeida Prado, Fernando; Schütz, Gunter M.

    2011-03-01

    We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems. We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing "jumpy" transition from non-ergodicity with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical results suggests how to drive a system from an undesired socio-economic equilibrium (e.g. high level of corruption) to a desirable one (low level of corruption).

  9. Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices.

    PubMed

    Strečka, Jozef; Ekiz, Cesur

    2015-05-01

    The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three interconnected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes upon increasing the coordination number of the underlying Husimi lattice. PMID:26066155

  10. Non-degenerated Ground States and Low-degenerated Excited States in the Antiferromagnetic Ising Model on Triangulations

    NASA Astrophysics Data System (ADS)

    Jiménez, Andrea

    2014-02-01

    We study the unexpected asymptotic behavior of the degeneracy of the first few energy levels in the antiferromagnetic Ising model on triangulations of closed Riemann surfaces. There are strong mathematical and physical reasons to expect that the number of ground states (i.e., degeneracy) of the antiferromagnetic Ising model on the triangulations of a fixed closed Riemann surface is exponential in the number of vertices. In the set of plane triangulations, the degeneracy equals the number of perfect matchings of the geometric duals, and thus it is exponential by a recent result of Chudnovsky and Seymour. From the physics point of view, antiferromagnetic triangulations are geometrically frustrated systems, and in such systems exponential degeneracy is predicted. We present results that contradict these predictions. We prove that for each closed Riemann surface S of positive genus, there are sequences of triangulations of S with exactly one ground state. One possible explanation of this phenomenon is that exponential degeneracy would be found in the excited states with energy close to the ground state energy. However, as our second result, we show the existence of a sequence of triangulations of a closed Riemann surface of genus 10 with exactly one ground state such that the degeneracy of each of the 1st, 2nd, 3rd and 4th excited energy levels belongs to O( n), O( n 2), O( n 3) and O( n 4), respectively.

  11. Translation-invariant p-adic quasi-Gibbs measures for the Ising-Vannimenus model on a Cayley tree

    NASA Astrophysics Data System (ADS)

    Mukhamedov, F. M.; Saburov, M. Kh.; Khakimov, O. Kh.

    2016-04-01

    We consider the p-adic Ising-Vannimenus model on the Cayley tree of order k = 2. This model contains nearest-neighbor and next-nearest-neighbor interactions. We investigate the model using a new approach based on measure theory ( in the p-adic sense) and describe all translation-invariant p-adic quasi-Gibbs measures associated with the model. As a consequence, we can prove that a phase transition exists in the model. Here, "phase transition" means that there exist at least two nontrivial p-adic quasi-Gibbs measures such that one is bounded and the other is unbounded. The methods used are inapplicable in the real case.

  12. 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.

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

    PubMed

    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 L(2)=128(2) for different system temperatures T. The latter were chosen from an interval enclosing the critical point T(c) 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.

  14. Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

    NASA Astrophysics Data System (ADS)

    Jurčišinová, E.; Jurčišin, M.

    2016-09-01

    The antiferromagnetic spin-1 Ising model is studied on the Husimi lattice constructed from elementary triangles with coordination number z  =  4. It is found that the model has a unique solution for arbitrary values of the magnetic field as well as for all temperatures. A detailed analysis of the magnetization is performed and it is shown that in addition to the standard plateau-like ground states, the model also contains well-defined single-point ground states related to definite values of the magnetic field. Exact values of the residual entropies for all ground states are found. The properties of the susceptibility and the specific heat of the model are also discussed. The existence of the Schottky-type behavior of the specific heat and the strong magnetocaloric effect for low enough temperatures and for the external magnetic field close to the values at which the single-point ground states exist are identified.

  15. Tricritical wetting in the two-dimensional Ising magnet due to the presence of localized non-magnetic impurities.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V

    2016-03-31

    Fixed vacancies (non-magnetic impurities) are placed along the centre of Ising strips in order to study the wetting behaviour in this confined system, by means of numerical simulations analysed with the aid of finite size scaling and thermodynamic integration methods. By considering strips of size L × M (L < M) where short-range competitive surface fields (H(s)) act along the M-direction, we observe localization-delocalization transitions of the interface between magnetic domains of different orientation (driven by the corresponding surface fields), which are the precursors of the wetting transitions that occur in the thermodynamic limit. By placing vacancies or equivalently non-magnetic impurities along the centre of the sample, we found that for low vacancy densities the wetting transitions are of second order, while by increasing the concentration of vacancies the transitions become of first order. Second- and first-order lines meet in tricritical wetting points (H(tric)(SW), T(tric)(W)), where H(tric)(SW) and T(Tric)(W) are the magnitude of the surface field and the temperature, respectively. In the phase diagram, tricritical points shift from the high temperature and weak surface field regime at large vacancy densities to the T --> 0, H(tric)(SW) --> 1 limit for low vacancy densities. By comparing the locations of the tricritical points with those corresponding to the case of mobile impurities, we conclude that in order to observe similar effects, in the latter the required density of impurities is much smaller (e.g. by a factor 3-5). Furthermore, a proper density of non magnetic impurities placed along the centre of a strip can effectively pin rather flat magnetic interfaces for suitable values of the competing surface fields and temperature. PMID:26910650

  16. Tricritical wetting in the two-dimensional Ising magnet due to the presence of localized non-magnetic impurities.

    PubMed

    Trobo, Marta L; Albano, Ezequiel V

    2016-03-31

    Fixed vacancies (non-magnetic impurities) are placed along the centre of Ising strips in order to study the wetting behaviour in this confined system, by means of numerical simulations analysed with the aid of finite size scaling and thermodynamic integration methods. By considering strips of size L × M (L < M) where short-range competitive surface fields (H(s)) act along the M-direction, we observe localization-delocalization transitions of the interface between magnetic domains of different orientation (driven by the corresponding surface fields), which are the precursors of the wetting transitions that occur in the thermodynamic limit. By placing vacancies or equivalently non-magnetic impurities along the centre of the sample, we found that for low vacancy densities the wetting transitions are of second order, while by increasing the concentration of vacancies the transitions become of first order. Second- and first-order lines meet in tricritical wetting points (H(tric)(SW), T(tric)(W)), where H(tric)(SW) and T(Tric)(W) are the magnitude of the surface field and the temperature, respectively. In the phase diagram, tricritical points shift from the high temperature and weak surface field regime at large vacancy densities to the T --> 0, H(tric)(SW) --> 1 limit for low vacancy densities. By comparing the locations of the tricritical points with those corresponding to the case of mobile impurities, we conclude that in order to observe similar effects, in the latter the required density of impurities is much smaller (e.g. by a factor 3-5). Furthermore, a proper density of non magnetic impurities placed along the centre of a strip can effectively pin rather flat magnetic interfaces for suitable values of the competing surface fields and temperature.

  17. Spin transport in a one-dimensional anisotropic Heisenberg model.

    PubMed

    Znidarič, Marko

    2011-06-01

    We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ. PMID:21702588

  18. Investigating a link between all-atom model simulation and the Ising-based theory on the helix-coil transition. II. Nonstationary properties

    NASA Astrophysics Data System (ADS)

    Takano, Mitsunori; Nakamura, Hironori K.; Nagayama, Kuniaki; Suyama, Akira

    2003-06-01

    The all-atom and the Ising-based models have both played their own roles to help our understanding of helix-coil transition. In this study, we address to what degree these two theoretical models can be consistent with each other in the nonstationary regime, complementing the preceding equilibrium study. We conducted molecular dynamics simulations of an all-atom model polyalanine chain and Monte Carlo simulations of a corresponding kinetic Ising chain. Nonstationary properties of each model were characterized through power spectrum, Allan variance, and autocorrelation analyses regarding the time course of a system order parameter. A clear difference was indicated between the two models: the Ising-based model showed a Lorentzian spectrum in the frequency domain and a single exponential form in the time domain, whereas the all-atom model showed a 1/f spectrum and a stretched exponential form. The observed stretched exponential form is in agreement with a very recent T-jump experiment. The effect of viscous damping on helix-coil dynamics was also studied. A possible source of the observed difference between the two models is discussed by considering the potential energy landscape, and the idea of dynamical disorder was introduced into the original Glauber model in the hope of bridging the gap between the two models. Other possible sources, e.g., the limitations of the Ising framework and the validity of the Markovian dynamics assumption, are also discussed.

  19. A generalized Ising model for studying alloy evolution under irradiation and its use in kinetic Monte Carlo simulations.

    PubMed

    Huang, Chen-Hsi; Marian, Jaime

    2016-10-26

    We derive an Ising Hamiltonian for kinetic simulations involving interstitial and vacancy defects in binary alloys. Our model, which we term 'ABVI', incorporates solute transport by both interstitial defects and vacancies into a mathematically-consistent framework, and thus represents a generalization to the widely-used ABV model for alloy evolution simulations. The Hamiltonian captures the three possible interstitial configurations in a binary alloy: A-A, A-B, and B-B, which makes it particularly useful for irradiation damage simulations. All the constants of the Hamiltonian are expressed in terms of bond energies that can be computed using first-principles calculations. We implement our ABVI model in kinetic Monte Carlo simulations and perform a verification exercise by comparing our results to published irradiation damage simulations in simple binary systems with Frenkel pair defect production and several microstructural scenarios, with matching agreement found. PMID:27541350

  20. A generalized Ising model for studying alloy evolution under irradiation and its use in kinetic Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Huang, Chen-Hsi; Marian, Jaime

    2016-10-01

    We derive an Ising Hamiltonian for kinetic simulations involving interstitial and vacancy defects in binary alloys. Our model, which we term ‘ABVI’, incorporates solute transport by both interstitial defects and vacancies into a mathematically-consistent framework, and thus represents a generalization to the widely-used ABV model for alloy evolution simulations. The Hamiltonian captures the three possible interstitial configurations in a binary alloy: A-A, A-B, and B-B, which makes it particularly useful for irradiation damage simulations. All the constants of the Hamiltonian are expressed in terms of bond energies that can be computed using first-principles calculations. We implement our ABVI model in kinetic Monte Carlo simulations and perform a verification exercise by comparing our results to published irradiation damage simulations in simple binary systems with Frenkel pair defect production and several microstructural scenarios, with matching agreement found.

  1. Star-triangle relation for a three-dimensional model

    SciTech Connect

    Bazhanov, V.V. Institute for High Eenrgy Physics, Protvino, Moscow Region ); Baxter, R.J. Australian National Univ., Canberra )

    1993-06-01

    The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. It is shown that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly. 20 refs., 4 figs.

  2. Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network.

    PubMed

    Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji

    2012-09-01

    We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.

  3. 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.

  4. Effect of further-neighbor interactions on the magnetization behaviors of the Ising model on a triangular lattice.

    PubMed

    Chen, J; Zhuo, W Z; Qin, M H; Dong, S; Zeng, M; Lu, X B; Gao, X S; Liu, J-M

    2016-09-01

    In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization M S, in addition to the well-known plateaus at 0, 1/3 and 1/2 of M S. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy. PMID:27356040

  5. Effect of further-neighbor interactions on the magnetization behaviors of the Ising model on a triangular lattice

    NASA Astrophysics Data System (ADS)

    Chen, J.; Zhuo, W. Z.; Qin, M. H.; Dong, S.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.

    2016-09-01

    In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization M S, in addition to the well-known plateaus at 0, 1/3 and 1/2 of M S. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy.

  6. Quantum Monte Carlo study of long-range transverse-field Ising models on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Humeniuk, Stephan

    2016-03-01

    Motivated by recent experiments with a Penning ion trap quantum simulator, we perform numerically exact Stochastic Series Expansion quantum Monte Carlo simulations of long-range transverse-field Ising models on a triangular lattice for different decay powers α of the interactions. The phase boundary for the ferromagnet is obtained as a function of α . For antiferromagnetic interactions, there is strong indication that the transverse field stabilizes a clock ordered phase with sublattice magnetization (M ,-M/2 ,-M/2 ) with unsaturated M <1 in a process known as "order by disorder" similar to the nearest-neighbor antiferromagnet on the triangular lattice. Connecting the known limiting cases of nearest-neighbor and infinite-range interactions, a semiquantitative phase diagram is obtained. Magnetization curves for the ferromagnet for experimentally relevant system sizes and with open boundary conditions are presented.

  7. Dynamic phase transition properties for the mixed spin-(1/2, 1) Ising model in an oscillating magnetic field

    NASA Astrophysics Data System (ADS)

    Ertaş, Mehmet; Keskin, Mustafa

    2015-08-01

    Herein we study the dynamic phase transition properties for the mixed spin-(1/2, 1) Ising model on a square lattice under a time-dependent magnetic field by means of the effective-field theory (EFT) with correlations based on Glauber dynamics. We present the dynamic phase diagrams in the reduced magnetic field amplitude and reduced temperature plane and find that the phase diagrams exhibit dynamic tricitical behavior, multicritical and zero-temperature critical points as well as reentrant behavior. We also investigate the influence of frequency (ω) and observe that for small values of ω the mixed phase disappears, but for high values it appears and the system displays reentrant behavior as well as a critical end point.

  8. ``Avalanches'' in the ground state of the 3D Gaussian random field Ising model driven by an external field

    NASA Astrophysics Data System (ADS)

    Frontera, Carlos; Vives, Eduard

    2002-08-01

    We present a numerical study of the exact ground states of the 3D Gaussian random field Ising model (G-RFIM) with an applied external field B. We combine a max-flow min-cut algorithm with an optimal procedure for determining all the ground states when B is swept from -∞ to ∞. The magnetization of finite lattices ( L3) is studied as a function of the degree of disorder in the system σ (standard deviation of the Gaussian random fields). The magnetization evolves as a sequence of jumps or "avalanches" with a certain size s. The statistical distribution p( s) becomes a power law p( s)˜ s- τ for a certain degree of disorder σc( L). The extrapolation of the results to L→∞ renders σc≃2.4±0.1 and τ≃1.70±0.07.

  9. Topological phases of shaken quantum Ising lattices

    NASA Astrophysics Data System (ADS)

    Fernández-Lorenzo, Samuel; José García-Ripoll, Juan; Porras, Diego

    2016-02-01

    The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those systems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.

  10. Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Bachschmid-Romano, L.; Battistin, C.; Opper, M.; Roudi, Y.

    2016-10-01

    We describe and analyze some novel approaches for studying the dynamics of Ising spin glass models. We first briefly consider the variational approach based on minimizing the Kullback–Leibler divergence between independent trajectories and the real ones and note that this approach only coincides with the mean field equations from the saddle point approximation to the generating functional when the dynamics is defined through a logistic link function, which is the case for the kinetic Ising model with parallel update. We then spend the rest of the paper developing two ways of going beyond the saddle point approximation to the generating functional. In the first one, we develop a variational perturbative approximation to the generating functional by expanding the action around a quadratic function of the local fields and conjugate local fields whose parameters are optimized. We derive analytical expressions for the optimal parameters and show that when the optimization is suitably restricted, we recover the mean field equations that are exact for the fully asymmetric random couplings (Mézard and Sakellariou 2011 J. Stat. Mech. 2011 L07001). However, without this restriction the results are different. We also describe an extended Plefka expansion in which in addition to the magnetization, we also fix the correlation and response functions. Finally, we numerically study the performance of these approximations for Sherrington–Kirkpatrick type couplings for various coupling strengths and the degrees of coupling symmetry, for both temporally constant but random, as well as time varying external fields. We show that the dynamical equations derived from the extended Plefka expansion outperform the others in all regimes, although it is computationally more demanding. The unconstrained variational approach does not perform well in the small coupling regime, while it approaches dynamical TAP equations of (Roudi and Hertz 2011 J. Stat. Mech. 2011 P03031) for strong

  11. Properties of Ising Networks

    NASA Astrophysics Data System (ADS)

    Zhang, Guihua

    1992-08-01

    Inhomogeneous Ising networks are studied in this thesis. Profile equations for Ising systems with inhomogeneous external fields and short range interactions are presented for simply-connected, closed chain and ring-like networks. The existence of generating functionals has been proved; for some special cases, the corresponding generating functionals are written out explicitly. The profile equations for a simply-connected system turns out to be a local form, in terms of local quantities like magnetizations and local correlations of two site magnetizations. For nonsimply-connected systems, additional collective mode variables are found which regain the localities of the profile equations. The collective variables take care of all the global effects from all the feedback loops. They enable us to treat the local and global aspects simultaneously. The statistical mechanics of a nonuniform nearest -neighbor interaction with four states per site is carried out and converted to that of a two state second-neighbor gas. A mixed density-potential representation is presented and the appropriate generating functional is constructed. Application is made to the site representation of a hydrogenmolecule -water mixture. A one dimensional spin glass is studied by using the entropy functional method; the integral equations for the effective field are rederived. The corresponding integral equations in magnetization space are established. Extension to a Bethe lattice is made. The thermodynamics of a classical lattice gas in Ising form, with arbitrary interaction, is set up in entropy format, with multipoint magnetizations as control parameters. It is specialized to the case of one and two -point interactions on a simply connected lattice; both entropy and profile equations are written down explicitly. Linear response functions are expressed in Wertheim-Baxter factorization and used to derive the Jacobian of the transformation from couplings to magnetizations. An arbitrary spin

  12. Comparison of the exact thermodynamics of the AF Blume-Emery-Grifiths and of the spin-1 ferromagnetic Ising models

    NASA Astrophysics Data System (ADS)

    Corrêa Silva, E. V.; Thomaz, M. T.

    2016-11-01

    We study in detail the thermodynamics of the anti-ferromagnetic Blume-Emery-Griffiths (AF BEG) model in the presence of a longitudinal magnetic field. Its thermodynamics is derived from the exact Helmholtz free energy (HFE) of the model, valid for T > 0. Numerical simulations of this model on a periodic space chain with 10 sites (N=10) yield the energy spectra of the model at K/J = 2 for D/J = 1 and D/J = 2, thus helping us compare, for a broad range of temperature, how some (per site) thermodynamic functions with the same value of K/J but distinct values of D/J behave, namely: the z-component of the magnetization, the specific heat and the entropy. These thermodynamic functions of the AF BEG model at K/|J| = 2 are compared to those of the spin-1 ferromagnetic Ising model with D/|J| > 1.5, for which the T=0 phase diagrams of both models are identical. This comparison is done in a large interval of temperature.

  13. Inverse Ising inference with correlated samples

    NASA Astrophysics Data System (ADS)

    Obermayer, Benedikt; Levine, Erel

    2014-12-01

    Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially, the parameters of the least constrained statistical model are learned from the observed correlations such that direct interactions can be separated from indirect correlations. Among many other applications, this approach has been helpful for protein structure prediction, because residues which interact in the 3D structure often show correlated substitutions in a multiple sequence alignment. In this context, samples used for inference are not independent but share an evolutionary history on a phylogenetic tree. Here, we discuss the effects of correlations between samples on global inference. Such correlations could arise due to phylogeny but also via other slow dynamical processes. We present a simple analytical model to address the resulting inference biases, and develop an exact method accounting for background correlations in alignment data by combining phylogenetic modeling with an adaptive cluster expansion algorithm. We find that popular reweighting schemes are only marginally effective at removing phylogenetic bias, suggest a rescaling strategy that yields better results, and provide evidence that our conclusions carry over to the frequently used mean-field approach to the inverse Ising problem.

  14. Four-particle decay of the Bethe-Salpeter kernel in the high-temperature Ising model

    NASA Astrophysics Data System (ADS)

    Auil, F.

    2002-12-01

    In this article we study the four-particle decay of the Bethe-Salpeter (B-S) kernel for the high-temperature Ising model. We use the hyperplane decoupling method [T. Spencer, Commun. Math. Phys. 44, 143 (1975); R. S. Schor, Nucl. Phys. B 222, 71 (1983)] to prove exponential decay in a set of variables particularly adapted to the methods of Spencer and Zirilli [Commun. Math. Phys. 49, 1 (1976)] for the analysis of scattering and bound states in QFT, transcribed to lattice theories by Auil and Barata [Ann. Henri Poincare 2, 1065 (2001)]. We study arbitrary derivatives of the general n-point correlation functions with respect to the interpolating variables, and we are able to obtain, in some cases, information about the third derivatives of the B-S kernel. As a later consequence, we have two-body asymptotic completeness for the (massive) Euclidean lattice field theory implemented by this model. This allows us to analyze the Ornstein-Zernike behavior of four-point functions, related to the specific heat of the model.

  15. Markov-Chain Monte Carlo Simulation of Inverse-Halftoning for Error Diffusion based on Statistical Mechanics of the Q-Ising Model

    NASA Astrophysics Data System (ADS)

    Saika, Yohei

    2008-02-01

    On the basis of statistical mechanics of the Q-Ising model we formulate the problem of inverse-halftoning for the halftone image which is obtained by the error diffusion method using the Floyd-Steinburg and two weight kernels. Then using the Markov-Chain Monte Carlo simulation both for a set of the snapshots of the Q-Ising model and a gray-level standard image, we estimate the performance of our method based on the mean square error and the edge structures observed both in the halftone image and reconstructed images, such as the edge length and the gradient of the gray-level. We clarify that our method reconstructs the gray-level image from the halftone image by suppressing the gradient of the gray-level on the edges embedded in the halftone image and by removing a part of the edges if we appropriately set parameters of our model.

  16. Role of further-neighbor interactions in modulating the critical behavior of the Ising model with frustration.

    PubMed

    Liu, R M; Zhuo, W Z; Dong, S; Lu, X B; Gao, X S; Qin, M H; Liu, J-M

    2016-03-01

    In this work, we investigate the phase transitions and critical behaviors of the frustrated J(1)-J(2)-J(3) Ising model on the square lattice using Monte Carlo simulations, and particular attention goes to the effect of the second-next-nearest-neighbor interaction J(3) on the phase transition from a disordered state to the single stripe antiferromagnetic state. A continuous Ashkin-Teller-like transition behavior in a certain range of J(3) is identified, while the four-state Potts-critical end point [J(3)/J(1)](C) is estimated based on the analytic method reported in earlier work [Jin, Sen, and Sandvik, Phys. Rev. Lett. 108, 045702 (2012)]. It is suggested that the interaction J(3) can tune the transition temperature and in turn modulate the critical behaviors of the frustrated model. Furthermore, it is revealed that an antiferromagnetic J(3) can stabilize the staggered dimer state via a phase transition of strong first-order character. PMID:27078299

  17. Truncated Wigner theory of coherent Ising machines based on degenerate optical parametric oscillator network

    NASA Astrophysics Data System (ADS)

    Maruo, Daiki; Utsunomiya, Shoko; Yamamoto, Yoshihisa

    2016-08-01

    We present the quantum theory of coherent Ising machines based on networks of degenerate optical parametric oscillators (DOPOs). In a simple model consisting of two coupled DOPOs, both positive-P representation and truncated Wigner representation predict quantum correlation and inseparability between the two DOPOs in spite of the open-dissipative nature of the system. Here, we apply the truncated Wigner representation method to coherent Ising machines with thermal, vacuum, and squeezed reservoir fields. We find that the probability of finding the ground state of a one-dimensional Ising model increases substantially as a result of reducing excess thermal noise and squeezing the incident vacuum fluctuation on the out-coupling port.

  18. Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

    NASA Astrophysics Data System (ADS)

    Sampaio Filho, C. I. N.; dos Santos, T. B.; Moreira, A. A.; Moreira, F. G. B.; Andrade, J. S.

    2016-05-01

    We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which directed long-range connections are randomly added according to the probability Pi j˜r-α , where ri j is the Manhattan distance between nodes i and j , and the exponent α is a controlling parameter [J. M. Kleinberg, Nature (London) 406, 845 (2000), 10.1038/35022643]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent α . Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For α ≤3 the critical behavior is described by mean-field exponents, while for α ≥4 it belongs to the Ising universality class. Finally, in the region where the crossover occurs, 3 <α <4 , the critical exponents are dependent on α .

  19. Monte Carlo entropic sampling applied to Ising-like model for 2D and 3D systems

    NASA Astrophysics Data System (ADS)

    Jureschi, C. M.; Linares, J.; Dahoo, P. R.; Alayli, Y.

    2016-08-01

    In this paper we present the Monte Carlo entropic sampling (MCES) applied to an Ising-like model for 2D and 3D system in order to show the interaction influence of the edge molecules of the system with their local environment. We show that, as for the 1D and the 2D spin crossover (SCO) systems, the origin of multi steps transition in 3D SCO is the effect of the edge interaction molecules with its local environment together with short and long range interactions. Another important result worth noting is the co-existence of step transitions with hysteresis and without hysteresis. By increasing the value of the edge interaction, L, the transition is shifted to the lower temperatures: it means that the role of edge interaction is equivalent to an applied negative pressure because the edge interaction favours the HS state while the applied pressure favours the LS state. We also analyse, in this contribution, the role of the short- and long-range interaction, J respectively G, with respect to the environment interaction, L.

  20. Experimental realization of the zero temperature Random Field Ising Model : the condensation of 4He in aerogels

    NASA Astrophysics Data System (ADS)

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

    2013-03-01

    Although widely studied, the effect of disorder on a first order phase transition is still highly debated. Numerical simulations of the T = 0 Random Field Ising Model show that magnetization evolves by avalanches, the average size of which diverges below a critical disorder (Sethna et al., PRL 70 3347 (1993)). Nevertheless, experimental evidence is scarce up to now (Berger et al., PRL 85, 4176 (2000)). In the case of the liquid gas transition in disordered porous media, the same theoretical concepts can be applied (Detcheverry et al., PRE 72 051506 (2005)). We have studied experimentally this phase transition using 4He in silica aerogels. Optical and thermodynamical measurements show that the condensation is an out of equilibrium process. We clearly observe two filling regimes separated by a critical temperature T* : below T*, filling is discontinuous (macro avalanche) whereas above T* it becomes continuous (micro avalanches). In addition, we have developed a speckle interferometry technique to detect single avalanches. We argue that our results support the disorder induced phase transition. This work was supported by ANR-06-BLAN-0098.

  1. Repulsive interactions induced by specific adsorption: Anomalous step diffusivity and inadequacy of nearest-neighbor Ising model. (part I experimental)

    NASA Astrophysics Data System (ADS)

    Al-Shakran, Mohammad; Kibler, Ludwig A.; Jacob, Timo; Ibach, Harald; Beltramo, Guillermo L.; Giesen, Margret

    2016-09-01

    This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data. As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ɛNN, ɛNNN) can uniquely be derived from the diffusivity of steps along <100> and <110>. We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ɛNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ɛNNN increases with increasing Br- and Cl- coverage. The results for ɛNN and ɛNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.

  2. Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe.

    PubMed

    Yu, Rong; Si, Qimiao

    2015-09-11

    Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments. PMID:26406842

  3. Ising formulations of many NP problems

    NASA Astrophysics Data System (ADS)

    Lucas, Andrew

    2014-02-01

    We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.

  4. Fractional magnetization plateaus of the spin-1/2 Heisenberg orthogonal-dimer chain: Strong-coupling approach developed from the exactly solved Ising-Heisenberg model

    NASA Astrophysics Data System (ADS)

    Verkholyak, Taras; Strečka, Jozef

    2016-10-01

    The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaus at zero, one-quarter, and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.

  5. An ISEE/Whistler model of equatorial electron density in the magnetosphere

    NASA Technical Reports Server (NTRS)

    Carpenter, D. L.; Anderson, R. R.

    1992-01-01

    Attention is given to an empirical model of equatorial electron density in the magnetosphere covering the L range 2.25-8. Although the model is primarily intended for application to the local time interval 00-15 MLT, a way to extend the model to the 15-24-MLT period is presented. The model describes, in piecewise fashion, the 'saturated' plasmasphere, the region of steep plasmapause gradients, and the plasma trough. Within the plasmasphere the model profile can be expressed as logne - Sigma-xi, where x1 = -0.3145L + 3.9043 is the principal or 'reference' term, and additional terms account for: a solar cycle variation with a peak at solar maximum; an annual variation with a December maximum; and a semiannual variation with equinoctial maxima.

  6. Large-scale Ising spin network based on degenerate optical parametric oscillators

    NASA Astrophysics Data System (ADS)

    Inagaki, Takahiro; Inaba, Kensuke; Hamerly, Ryan; Inoue, Kyo; Yamamoto, Yoshihisa; Takesue, Hiroki

    2016-06-01

    Solving combinatorial optimization problems is becoming increasingly important in modern society, where the analysis and optimization of unprecedentedly complex systems are required. Many such problems can be mapped onto the ground-state-search problem of the Ising Hamiltonian, and simulating the Ising spins with physical systems is now emerging as a promising approach for tackling such problems. Here, we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPOs), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generate >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing in a highly nonlinear fibre placed in a cavity. Using those DOPOs, a one-dimensional Ising model is simulated by introducing nearest-neighbour optical coupling. We observe the formation of spin domains and find that the domain size diverges near the DOPO threshold, which suggests that the DOPO network can simulate the behaviour of low-temperature Ising spins.

  7. A haplotype inference method based on sparsely connected multi-body ising model

    NASA Astrophysics Data System (ADS)

    Kato, Masashi; Gao, Qian Ji; Chigira, Hiroshi; Shindo, Hiroyuki; Inoue, Masato

    2010-06-01

    Statistical haplotype inference is an indispensable technique in the field of medical science. The method usually has two steps: inference of haplotype frequencies and inference of diplotype for each subject. The first step can be done by using the expectation-maximization (EM) algorithm, but it incurs an unreasonably large calculation cost when the number of single-nucleotide polymorphism (SNP) loci of concern is large. In this article, we describe an approximate probabilistic model of haplotype frequencies. The model is constructed by using several distributions of nearby local SNPs. This approximation seems good because SNPs are generally more strongly correlated when they are close to one another on a chromosome. To implement this approach, we use a log linear model, the Walsh-Hadamard transform, and a combinatorial optimization method. Artificial data suggested that the overall haplotype inference of our method is good if there are nine or more local consecutive SNPs. Some minor problems should be dealt with before this method can be applied to real data.

  8. Ising-based model of opinion formation in a complex network of interpersonal interactions

    NASA Astrophysics Data System (ADS)

    Grabowski, A.; Kosiński, R. A.

    2006-03-01

    In our work the process of opinion formation in the human population, treated as a scale-free network, is modeled and investigated numerically. The individuals (nodes of the network) are characterized by their authorities, which influence the interpersonal interactions in the population. Hierarchical, two-level structures of interpersonal interactions and spatial localization of individuals are taken into account. The effect of the mass media, modeled as an external stimulation acting on the social network, on the process of opinion formation is investigated. It was found that in the time evolution of opinions of individuals critical phenomena occur. The first one is observed in the critical temperature of the system TC and is connected with the situation in the community, which may be described by such quantifiers as the economic status of people, unemployment or crime wave. Another critical phenomenon is connected with the influence of mass media on the population. As results from our computations, under certain circumstances the mass media can provoke critical rebuilding of opinions in the population.

  9. Quantum simulation with arrays of transmon qubits: Ising dynamics

    NASA Astrophysics Data System (ADS)

    Ramasesh, Vinay; Hacohen-Gourgy, Shay; Kiendl, Thomas; Marquardt, Florian; Siwak, Nathan; Richardson, Christopher; Siddiqi, Irfan

    2015-03-01

    Chains of coupled qubits are known to realize the transverse-field Ising Hamiltonian in the two-level approximation. In this model, the qubit transition frequencies map onto the external magnetic field, so the ground and excited states play the role of spin-up and spin-down atoms. We implement this structure in a planar, on-chip architecture, with a one dimensional linear array of capacitively-coupled transmon qubits, where the two terminal qubits are dispersively coupled to microwave independent resonators for state readout. We present spectroscopic data and describe coherent manipulations in the array. This work is supported by the AFOSR.

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

    SciTech Connect

    Murtazaev, A. K.; Ramazanov, M. K.; Kassan-Ogly, F. A.; Kurbanova, D. R.

    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.

  11. Functional scale-free networks in the two-dimensional Abelian sandpile model

    NASA Astrophysics Data System (ADS)

    Zarepour, M.; Niry, M. D.; Valizadeh, A.

    2015-07-01

    Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010), 10.1038/nphys1803]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.

  12. Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains.

    PubMed

    Ivanov, Dmitri A; Abanov, Alexander G

    2013-02-01

    We propose to describe correlations in classical and quantum systems in terms of full counting statistics of a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the classical one-dimensional Ising model and the quantum spin-1/2 XY chain. For the one-dimensional Ising model, our method results in a phase diagram with two phases distinguishable by the long-distance behavior of the Jordan-Wigner strings. For the anisotropic spin-1/2 XY chain in a transverse magnetic field, we compute the full counting statistics of the magnetization and use it to classify quantum phases of the chain. The method, in this case, reproduces the previously known phase diagram. We also discuss the relation between our approach and the Lee-Yang theory of zeros of the partition function. PMID:23496467

  13. Spin-wave Response in the Dilute Quasi-one-dimensional Ising-Like Antiferromagnet CsCo0.83Mg0.17Br3

    SciTech Connect

    Yang, Y. S.; Marsiglio, F.; Madsen, M.; Gaulin, Bruce D.; Rogge, R. B.; Fernandez-Baca, Jaime A

    2002-01-01

    Inelastic neutron-scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo{sub 0.83}Mg{sub 0.17}Br{sub 3} have been investigated. Calculations of S{sup xx}(Q,{omega}), based on an effective spin Hamiltonian, accurately describe the experimental spin-wave spectrum of the 2J mode. The Q dependence of the energy of this spin-wave mode follows the analytical prediction {omega}{sub xx}(Q)=(2J)(1-5{var_epsilon}{sup 2}cos{sup 2}Qa+2{var_epsilon}{sup 2}){sup 1/2}, calculated by Ishimura and Shiba using perturbation theory.

  14. Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field

    SciTech Connect

    Fritsch, Katharina; Ehlers, G.; Rule, K. C.; Habicht, Klaus; Ramazanoglu, Mehmet K.; Dabkowska, H. A.; Gaulin, Bruce D.

    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, Co3V2O8, 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 μ0Hc1~6.25 T and μ0Hc2~7 T is discontinuous, while the final quantum critical point at μ0Hc3~13 T is continuous.

  15. Quantum Phase Transitions and De-Coupling of Magnetic Sublattices in the Quasi-Two Dimensional Ising Magnet Co3V2O8 in a Transverse Magnetic Field

    NASA Astrophysics Data System (ADS)

    Fritsch, K.; Ehlers, G.; Rule, K. C.; Habicht, K.; Ramazanoglu, M.; Dabkowska, H. A.; Gaulin, B. D.

    2015-03-01

    The application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two dimensional Kagome staircase magnet, Co3V2O8, 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 allows the mapping of a sequence of ferromagnetic and incommensurate phases and their accompanying spin excitations. At least one of the transitions to incommensurate phases at μ0Hc 1 ~ 6 . 25 T and μ0Hc 2 ~ 7 T are discontinuous, while the final quantum critical point at μ0Hc 3 ~ 13 T is continuous.

  16. Aneesur Rahman Prize: The Inverse Ising Problem

    NASA Astrophysics Data System (ADS)

    Swendsen, Robert

    2014-03-01

    Many methods are available for carrying out computer simulations of a model Hamiltonian to obtain thermodynamic information by generating a set of configurations. The inverse problem consists of recreating the parameters of the Hamiltonian, given a set of configurations. The problem arises in a variety of contexts, and there has been much interest recently in the inverse Ising problem, in which the configurations consist of Ising spins. I will discuss an efficient method for solving the problem and what it can tell us about the Sherrington-Kirkpatrick model.

  17. Ising, Schelling and self-organising segregation

    NASA Astrophysics Data System (ADS)

    Stauffer, D.; Solomon, S.

    2007-06-01

    The similarities between phase separation in physics and residential segregation by preference in the Schelling model of 1971 are reviewed. Also, new computer simulations of asymmetric interactions different from the usual Ising model are presented, showing spontaneous magnetisation (=self-organising segregation) and in one case a sharp phase transition.

  18. Nagoya, Ise Bay, Japan

    NASA Technical Reports Server (NTRS)

    1982-01-01

    This view of Nagoya, Ise Bay and nearby Kyoto, on the main island of Honshu, Japan (35.0N, 137.0E) combines in a single photo both the political, cultural and educational centers of early Japan as well as one of the main educational and business centers of modern Japan. Besides being a business, cultural and educational center, Nagoya is near the geographic center of the Japanese home islands.

  19. Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

    NASA Astrophysics Data System (ADS)

    Wittmann, Matthew; Yucesoy, B.; Katzgraber, Helmut G.; Machta, J.; Young, A. P.

    2014-10-01

    Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and four space dimensions, and one-dimensional long-range models with diluted power-law interactions. We study three long-range models with different powers as follows: The first is approximately equivalent to a short-range model in three dimensions, the second to a short-range model in four dimensions, and the third to a short-range model in the mean-field regime. We study an observable proposed earlier by some of us which aims to distinguish the "replica symmetry breaking" picture of the spin-glass phase from the "droplet picture," finding that larger system sizes would be needed to unambiguously determine which of these pictures describes the low-temperature state of spin glasses best, except for the Sherrington-Kirkpatrick model, which is unambiguously described by replica symmetry breaking. Finally, we also study the median integrated overlap probability distribution and a typical overlap distribution, finding that these observables are not particularly helpful in distinguishing the replica symmetry breaking and the droplet pictures.

  20. Simulating Ising spin glasses on a quantum computer

    NASA Astrophysics Data System (ADS)

    Lidar, Daniel A.; Biham, Ofer

    1997-09-01

    A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum probability equal to the corresponding thermodynamic weight. The partition function is thus approximated efficiently. The algorithm neither suffers from critical slowing down nor gets stuck in local minima. The algorithm can be applied in any dimension, to a class of spin-glass Ising models with a finite portion of frustrated plaquettes, diluted Ising models, and models with a magnetic field.

  1. Magnetic properties of an Ising ferromagnetic model on a square lattice with next-nearest-neighbor and crystal field interactions

    NASA Astrophysics Data System (ADS)

    De La Espriella, N.; Arenas, Abraham J.; Páez Meza, M. S.

    2016-11-01

    We studied an Ising ferromagnet on a bipartite square lattice with nearest-neighbor ferromagnetic exchange couplings between spin values SiA = 2 and σjB = 5 / 2, next-nearest-neighbor exchange couplings between spins, SiA = 2 and an average term of single-ion anisotropy for each lattice site. We carried out Monte Carlo simulations on the planes (D‧ ,kB T‧) and (J2‧ ,kB T‧) to investigate the influence of exchange parameters J2‧ and anisotropy of D‧ lattice on the critical temperature of the system. The thermal behaviors of the sublattice magnetizations, total magnetization and specific heat were investigated. We found that the critical behavior system depends linearly on the next-nearest-neighbor interaction J2‧ and for antiferromagnetic exchange interactions the system undergoes reentrant phenomena.

  2. An Ising-like Model to Predict Dielectric Properties of the Relaxor Ferroelectric Solid Solution Barium titanate - Bismuth(Zinc1/2Titanium 1/2)Oxide

    NASA Astrophysics Data System (ADS)

    Jackson, Dennis L.

    We developed a model to investigate the dielectric properties of the BaTiO3 - Bi(Zn 1/2Ti1/2)O3 (BT-BZT) solid solution, which is a relaxor ferroelectric and exhibits long range disorder. The model uses ab initio methods to determine all polarization states for every atomic configuration of 2x2x2 supercells of BT-BZT. Each supercell is placed on a lattice with an Ising-like interaction between neighboring cell polarizations. This method allows us to consider long range disorder, which is not possible with ab initio methods alone, and is required to properly understand relaxor ferroelectric materials. We analyze the Monte Carlo data for a single lattice configuration using the multiple histogram method, and develop a modified histogram technique to combine data from multiple lattice configurations. Our calculated values of dielectric constant, specific heat, and polarization agree reasonably well with experiment.

  3. Spatially clustered zealots in a two-dimensional voter model

    NASA Astrophysics Data System (ADS)

    Stone, Thomas; Ludden, Matthew; McKay, Susan

    The voter model, solvable in all dimensions in its standard form, has been extensively used to study behavior dynamics by using the tools of statistical mechanics. Recently, much work has been focused on determining the effects of zealots in the voter model, where a zealot is an agent that maintains its opinion (akin to an Ising spin variable) no matter the local environment. Here we investigate the effects of spatially clustered zealots in the standard voter model on a two-dimensional square lattice. The clustering of zealots is quantified by the conditional probability that a zealot of the +1 state appears on an adjacent site to a randomly chosen zealot. (All zealots are of the +1 state.) We determine the functional forms of the system consensus time with respect to system size, clustering, and zealot density, and compare these findings to previous results that do not include clustering. We also discuss an interesting random walk problem that arises when one attempts to calculate how clustering affects the consensus time for fixed zealot density and system size.

  4. 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.

  5. Critical behaviors of transverse crystal field and bimodal magnetic field mixed spin Ising model with bond dilution or bond percolation threshold

    NASA Astrophysics Data System (ADS)

    Xu, C. Q.; Yan, S. L.

    2016-10-01

    Within the effective field theory, we investigate critical behaviors of transverse crystal field and bimodal magnetic field mixed spin-1/2 and spin-1 Ising model with bond dilution or percolation threshold on a simple cubic lattice. A-type double tricritical points and zigzag reentrant phenomenon can be found at pure bond and large bimodal magnetic field status. The ordered phase is impaired sharply due to bond dilution. The positive transverse crystal field can induce ordered phase at ordinary bond percolation threshold. The bimodal magnetic field can suppress the induced ordered phase and form a series of closed ordered regions. An extraordinary bond percolation threshold is determined, at which the induced ordered phase vanishes completely. The different effects of bimodal magnetic field and bond percolation threshold on induced ordered phase are discussed.

  6. Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model

    NASA Astrophysics Data System (ADS)

    Alonso, Juan J.; Fernández, Julio F.

    2010-02-01

    By tempered Monte Carlo simulations, we study site-diluted Ising systems of magnetic dipoles. All dipoles are randomly placed on a fraction x of all L3 sites of a simple cubic lattice, and point along a given crystalline axis. For xc

  7. Thermal hysteresis kinetic effects of spin crossover nanoparticulated systems studied by FORC diagram method on an Ising-like model

    NASA Astrophysics Data System (ADS)

    Atitoaie, Alexandru; Stoleriu, Laurentiu; Tanasa, Radu; Stancu, Alexandru; Enachescu, Cristian

    2016-04-01

    The scientific community is manifesting a high research interest on spin crossover compounds and their recently synthesized nanoparticles, due to their various appealing properties, such as the bistability between a diamagnetic low spin state and a paramagnetic high spin state (HS), inter-switchable by temperature or pressure changes, light irradiation or magnetic field. The utility of these compounds showing hysteresis covers a broad area of applications, from the development of more efficient designs of temperature and pressure sensors to automotive and aeronautic industries and even a new type of molecular actuators. We are proposing in this work a study regarding the kinetic effects and the distribution of reversible and irreversible components on the thermal hysteresis of spin crossover nanoparticulated systems. We are considering here tridimensional systems with different sizes and also systems of nanoparticles with a Gaussian size distribution. The correlations between the kinetics of the thermal hysteresis, the distributions of sizes and intermolecular interactions and the transition temperature distributions were established by using the FORC (First Order Reversal Curves) method using a Monte Carlo technique within an Ising-like system.

  8. Robustness of topological quantum codes: Ising perturbation

    NASA Astrophysics Data System (ADS)

    Zarei, Mohammad Hossein

    2015-02-01

    We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by rewriting the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.

  9. One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization

    NASA Astrophysics Data System (ADS)

    Brzezicki, Wojciech; Oleś, Andrzej M.

    2016-06-01

    We introduce a one-dimensional (1D) pseudospin model on a ladder where the Ising interactions along the legs and along the rungs alternate between XiXi +1 and ZiZi +1 for even/odd bond (rung). We include also the next-nearest-neighbor Ising interactions on plaquettes' diagonals that alternate in such a way that a model where only leg interactions are switched on is equivalent to the one when only the diagonal ones are present. Thus in the absence of rung interactions the model can interpolate between two 1D compass models. The model possesses local symmetries which are the parities within each 2 ×2 cell (plaquette) of the ladder. We find that for different values of the interaction it can realize ground states that differ by the patterns formed by these local parities. By exact diagonalization we derive detailed phase diagrams for small systems of L =4 , 6, and 8 plaquettes, and use next L =12 to identify generic phases that appear in larger systems as well. Among them we find a nematic phase with macroscopic degeneracy when the leg and diagonal interactions are equal and the rung interactions are larger than a critical value. By performing a perturbative expansion around this phase we find indeed a very complex competition around the nematic phase which has to do with releasing frustration in this range of parameters. The nematic phase is similar to the one found in the two-dimensional compass model. For particular parameters the low-energy sector of the present plaquette model reduces to a 1D compass model with spins S =1 which suggests that it realizes peculiar crossovers within the class of compass models. Finally, we show that the model can realize phases with broken translation invariance which can be either dimerized, trimerized, etc., or completely disordered and highly entangled in a well identified window of the phase diagram.

  10. Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions.

    PubMed

    Fytas, Nikolaos G; Martín-Mayor, Víctor

    2016-06-01

    It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used. PMID:27415388

  11. Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

    NASA Astrophysics Data System (ADS)

    Fytas, Nikolaos G.; Martín-Mayor, Víctor

    2016-06-01

    It was recently shown [Phys. Rev. Lett. 110, 227201 (2013), 10.1103/PhysRevLett.110.227201] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero- and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent α of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

  12. Sparse High Dimensional Models in Economics.

    PubMed

    Fan, Jianqing; Lv, Jinchi; Qi, Lei

    2011-09-01

    This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635

  13. Sparse High Dimensional Models in Economics

    PubMed Central

    Fan, Jianqing; Lv, Jinchi; Qi, Lei

    2010-01-01

    This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance. Recent developments of theory, methods, and implementations in penalized least squares and penalized likelihood methods are highlighted. These variable selection methods are proved to be effective in high dimensional sparse modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in ultra-high dimensional sparse modeling are also briefly discussed. PMID:22022635

  14. Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm.

    PubMed

    Nonomura, Yoshihiko; Tomita, Yusuke

    2016-01-01

    Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)JUPSAU0031-901510.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies. PMID:26871018

  15. Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm

    NASA Astrophysics Data System (ADS)

    Nonomura, Yoshihiko; Tomita, Yusuke

    2016-01-01

    Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014), 10.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D X Y model. The critical exponents evaluated in the present study are consistent with those in previous studies.

  16. Integrals of the Ising Class

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.

    2006-06-01

    From an experimental-mathematical perspective we analyze"Ising-class" integrals. Our experimental results involvedextreme-precision, multidimensional quadrature on intricate integrands;thus, highly parallel computation was required.

  17. Ferrimagnetic behaviors in a transverse Ising nanoisland

    NASA Astrophysics Data System (ADS)

    Kaneyoshi, T.

    2016-05-01

    In this paper, the phase diagrams and magnetizations of a magnetic nanoisland described by the transverse Ising model (TIM) are investigated by the use of the effective-field theory (EFT) with correlations. A lot of characteristic behaviors observed in standard ferrimagnetic materials as well as novel phenomena have been obtained, although the system consists of two finite spin-1/2 layers coupled antiferromagnetically with a negative interlayer coupling.

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

    NASA Astrophysics Data System (ADS)

    Yunus, ćaǧın; Renklioǧlu, Başak; Keskin, Mustafa; Berker, A. Nihat

    2016-06-01

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

  19. Frustration in an exactly solvable mixed-spin Ising model with bilinear and three-site four-spin interactions on a decorated square lattice

    NASA Astrophysics Data System (ADS)

    Jaščur, M.; Štubňa, V.; Szałowski, K.; Balcerzak, T.

    2016-11-01

    Competitive effects of so-called three-site four-spin interactions, single ion anisotropy and bilinear interactions is studied in the mixed spin-1/2 and spin-1 Ising model on a decorated square lattice. Exploring the decoration-iteration transformation, we have obtained exact closed-form expressions for the partition function and other thermodynamic quantities of the model. From these relations, we have numerically determined ground-state and finite-temperature phase diagrams of the system. We have also investigated temperature variations of the correlation functions, internal energy, entropy, specific heat and Helmholtz free energy of the system. From the physical point of view, the most interesting result represents our observation of a partially ordered ferromagnetic or phase in the system with zero bilinear interactions. It is remarkable, that due to strong frustrations disordered spins survive in the system even at zero temperature, so that the ground state of the system becomes macroscopically degenerate with non-zero entropy. Introduction of arbitrarily small bilinear interaction completely removes degeneracy and the entropy always goes to zero at the ground state.

  20. Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg

    NASA Astrophysics Data System (ADS)

    Billoire, Alain; Campbell, I. A.

    2011-08-01

    A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass (ISG) model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t)˜exp{-[t/τ(T)]β(T)} with an exponent β(T) tending to ≈1/3 at Tg. The results are compared to those which were observed by A. T. Ogielski, [Phys. Rev. BPLRBAQ1098-012110.1103/PhysRevB.32.7384 32, 7384 (1985)] in the three-dimensional ISG model and are discussed in terms of a phase space percolation transition scenario.

  1. Ground State Properties of Ising Chain with Random Monomer-Dimer Couplings

    NASA Astrophysics Data System (ADS)

    Ardebili, S. Bahareh Seyedein; Sepehrinia, Reza

    2016-05-01

    We study analytically the one-dimensional Ising model with a random binary distribution of ferromagnetic and antiferromagnetic exchange couplings at zero temperature. We introduce correlations in the disorder by assigning a dimer of one type of coupling with probability x, and a monomer of the other type with probability 1-x. We find that the magnetization behaves differently from the original binary model. In particular, depending on which type of coupling comes in dimers, magnetization jumps vanish at a certain set of critical fields. We explain the results based on the structure of ground state spin configuration.

  2. Complexity and Ability in Ising Games

    NASA Astrophysics Data System (ADS)

    Ramirez, Ayax; George, Michael

    2008-03-01

    In previous work [1, 2], we discussed various facets of designs in games, and considered the evolution [2] of Ising games. The traditional aspect of game theory, with its focus on rational decisions, was not considered in this work. Instead, there was a predominant interest in the time evolution of design toward a goal design, and resulting levels of frustration. There was also a concern with time- reversal properties. In the new work, our goal is to consider the molecular structureof the Ising model as it evolves, and to associate this molecular structure with feedback into the structure that can be understood in algorithmic terms. We develop an analogy with the famous Malthusian argument concerning exponential population increase, associating ability to cope with complexity, and algorithmic complexity, and discuss biological implications of the ideas associated with these games. [1] M. George, A nonequilibrium statistical model based on latin squares, paper presented at WorldComp'07, Las Vegas, Nevada, June 25-28, 2007. [2] M. George, Classical and quantum Ising games, paper presented at Fourth International Conference in Applied Mathematics and Computing, Plovdiv, Bulgaria, August, 2007.

  3. Extra-dimensional models on the lattice

    DOE PAGES

    Knechtli, Francesco; Rinaldi, Enrico

    2016-08-05

    In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime formore » various extra-dimensional models.« less

  4. Existence of a dynamic compensation temperature of the mixed spin-1 and spin-3/2 Ising model within the effective-field theory

    NASA Astrophysics Data System (ADS)

    Shi, Xiaoling; Qi, Yang

    2015-07-01

    The effective-field theory with correlations based on Glauber-type stochastic dynamic is used to study the dynamic compensation behavior of the mixed spin-1 and spin-3/2 ferrimagnetic Ising model. The system is a layered honeycomb structure in which two kinds of spins (spin-1 and spin-3/2) occupy sites alternately. This is related to the experimental works of a molecular-based magnetic multilayer film, AMIIFeII(C2O4)3(A = N(n -CnH 2 n + 1) 4 ,MII = Mn,Fe) . The system is in the presence of a sinusoidal oscillating magnetic field and the Glauber dynamic is used to describe the time evolution of the system. The effects of the interlayer coupling and a crystal-field constant of the spin-1 sublattice on the compensation temperature are investigated. Dynamic phase diagrams, including the compensation points are presented. Besides second-order phase transition, lines of first-order phase transition, the dynamic tricritical point, the dynamic zero-temperature critical point and the multicritical point are found. The dynamic tricritical point, the dynamic compensation point and the non-magnetic phase predicted by the mean-field theory are confirmed by the effective-field theory.

  5. Influence of disorder on ageing and memory effects in non-equilibrium critical dynamics of 3D Ising model relaxing from an ordered state

    NASA Astrophysics Data System (ADS)

    Prudnikov, Vladimir V.; Prudnikov, Pavel V.; Pospelov, Evgeny A.

    2016-04-01

    We have performed a numerical investigation of the influence of disorder on the dynamical non-equilibrium evolution of a 3D site-diluted Ising model from a low-temperature initial state with magnetization m 0  =  1. It is shown that two-time dependences of the autocorrelation and integrated response functions for systems with spin concentrations p  =  1.0, 0.95, 0.8, 0.6 and 0.5 demonstrate ageing properties with anomalous slowing-down relaxation and violation of the fluctuation-dissipation ratio. It was revealed that during non-equilibrium critical dynamics in the long-time regime t-{{t}\\text{w}}\\gg {{t}\\text{w}}\\gg 1 the autocorrelation functions for diluted systems are extremely slow due to the pinning of domain walls on impurity sites. We have found that the fluctuation-dissipation ratio {{X}∞}=0 for diluted systems with spin concentration p  <  1 while the pure system is characterized by {{X}∞}=0.784(7) . The autocorrelation function power-law delay becomes the same as for the time dependence of the magnetization in the critical point and is characterized by exponent -β /zν . Also, for diluted systems we reveal memory effects for critical evolution in the ageing regime with realization of cyclic temperature change and quenching at T<{{T}\\text{c}} .

  6. Excitations in the quantum paramagnetic phase of the quasi-one-dimensional Ising magnet CoNb2O6 in a transverse field: Geometric frustration and quantum renormalization effects

    NASA Astrophysics Data System (ADS)

    Cabrera, Ivelisse; Thompson, J. D.; Coldea, R.; Prabhakaran, D.; Bewley, R. I.; Guidi, T.; Rodriguez-Rivera, J. A.; Stock, C.

    We report extensive single-crystal inelastic neutron scattering measurements of the magnetic excitations in the quasi 1D Ising ferromagnet CoNb2O6 in the quantum paramagnetic phase to characterize the effects of the finite interchain couplings. In this phase, we observe that excitations have a sharp, resolution-limited line shape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parametrized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than that predicted by a linear spin-wave model using exchange values determined at zero field. We attribute this effect to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant. We acknowledge support from EPSRC Grant No. EP/H014934/1, the Oxford Clarendon Fund Scholarship and NSERC of Canada.

  7. Bayesian Methods for High Dimensional Linear Models

    PubMed Central

    Mallick, Himel; Yi, Nengjun

    2013-01-01

    In this article, we present a selective overview of some recent developments in Bayesian model and variable selection methods for high dimensional linear models. While most of the reviews in literature are based on conventional methods, we focus on recently developed methods, which have proven to be successful in dealing with high dimensional variable selection. First, we give a brief overview of the traditional model selection methods (viz. Mallow’s Cp, AIC, BIC, DIC), followed by a discussion on some recently developed methods (viz. EBIC, regularization), which have occupied the minds of many statisticians. Then, we review high dimensional Bayesian methods with a particular emphasis on Bayesian regularization methods, which have been used extensively in recent years. We conclude by briefly addressing the asymptotic behaviors of Bayesian variable selection methods for high dimensional linear models under different regularity conditions. PMID:24511433

  8. Bayesian Methods for High Dimensional Linear Models.

    PubMed

    Mallick, Himel; Yi, Nengjun

    2013-06-01

    In this article, we present a selective overview of some recent developments in Bayesian model and variable selection methods for high dimensional linear models. While most of the reviews in literature are based on conventional methods, we focus on recently developed methods, which have proven to be successful in dealing with high dimensional variable selection. First, we give a brief overview of the traditional model selection methods (viz. Mallow's Cp, AIC, BIC, DIC), followed by a discussion on some recently developed methods (viz. EBIC, regularization), which have occupied the minds of many statisticians. Then, we review high dimensional Bayesian methods with a particular emphasis on Bayesian regularization methods, which have been used extensively in recent years. We conclude by briefly addressing the asymptotic behaviors of Bayesian variable selection methods for high dimensional linear models under different regularity conditions.

  9. Scaling of entanglement entropy in a quantum phase transition in the transverse Ising model induced by a quench

    SciTech Connect

    Majumdar, Priyadarshi; Bandyopadhyay, Pratul

    2010-01-15

    It is known that at the critical point of a zero-temperature quantum phase transition in a one-dimensional spin system the entanglement entropy of a block of L spins with the rest of the system scales logarithmically with L with a prefactor determined by the central charge of the relevant conformal field theory. When we introduce critical slowing down incorporating the Kibble-Zurek mechanism of defect formation induced by a quench, the implicit nonadiabatic transition disturbs the scaling behavior. We have shown that in this case the entanglement entropy also obeys a scaling law such that it increases logarithmically with L but the prefactor depends on the quench time. This puts a constraint on the block size L so that we cannot arbitrarily choose it. Thus, the entanglement entropy obeys the scaling law only in a restrictive sense due to the formation of defects.

  10. Solution Structure of IseA, an Inhibitor Protein of dl-Endopeptidases from Bacillus subtilis, Reveals a Novel Fold with a Characteristic Inhibitory Loop*

    PubMed Central

    Arai, Ryoichi; Fukui, Sadaharu; Kobayashi, Naoya; Sekiguchi, Junichi

    2012-01-01

    In Bacillus subtilis, LytE, LytF, CwlS, and CwlO are vegetative autolysins, dl-endopeptidases in the NlpC/P60 family, and play essential roles in cell growth and separation. IseA (YoeB) is a proteinaceous inhibitor against the dl-endopeptidases, peptidoglycan hydrolases. Overexpression of IseA caused significantly long chained cell morphology, because IseA inhibits the cell separation dl-endopeptidases post-translationally. Here, we report the first three-dimensional structure of IseA, determined by NMR spectroscopy. The structure includes a single domain consisting of three α-helices, one 310-helix, and eight β-strands, which is a novel fold like a “hacksaw.” Noteworthy is a dynamic loop between β4 and the 310-helix, which resembles a “blade.” The electrostatic potential distribution shows that most of the surface is positively charged, but the region around the loop is negatively charged. In contrast, the LytF active-site cleft is expected to be positively charged. NMR chemical shift perturbation of IseA interacting with LytF indicated that potential interaction sites are located around the loop. Furthermore, the IseA mutants D100K/D102K and G99P/G101P at the loop showed dramatic loss of inhibition activity against LytF, compared with wild-type IseA, indicating that the β4–310 loop plays an important role in inhibition. Moreover, we built a complex structure model of IseA-LytF by docking simulation, suggesting that the β4–310 loop of IseA gets stuck deep in the cleft of LytF, and the active site is occluded. These results suggest a novel inhibition mechanism of the hacksaw-like structure, which is different from known inhibitor proteins, through interactions around the characteristic loop regions with the active-site cleft of enzymes. PMID:23091053

  11. Solution structure of IseA, an inhibitor protein of DL-endopeptidases from Bacillus subtilis, reveals a novel fold with a characteristic inhibitory loop.

    PubMed

    Arai, Ryoichi; Fukui, Sadaharu; Kobayashi, Naoya; Sekiguchi, Junichi

    2012-12-28

    In Bacillus subtilis, LytE, LytF, CwlS, and CwlO are vegetative autolysins, DL-endopeptidases in the NlpC/P60 family, and play essential roles in cell growth and separation. IseA (YoeB) is a proteinaceous inhibitor against the DL-endopeptidases, peptidoglycan hydrolases. Overexpression of IseA caused significantly long chained cell morphology, because IseA inhibits the cell separation DL-endopeptidases post-translationally. Here, we report the first three-dimensional structure of IseA, determined by NMR spectroscopy. The structure includes a single domain consisting of three α-helices, one 3(10)-helix, and eight β-strands, which is a novel fold like a "hacksaw." Noteworthy is a dynamic loop between β4 and the 3(10)-helix, which resembles a "blade." The electrostatic potential distribution shows that most of the surface is positively charged, but the region around the loop is negatively charged. In contrast, the LytF active-site cleft is expected to be positively charged. NMR chemical shift perturbation of IseA interacting with LytF indicated that potential interaction sites are located around the loop. Furthermore, the IseA mutants D100K/D102K and G99P/G101P at the loop showed dramatic loss of inhibition activity against LytF, compared with wild-type IseA, indicating that the β4-3(10) loop plays an important role in inhibition. Moreover, we built a complex structure model of IseA-LytF by docking simulation, suggesting that the β4-3(10) loop of IseA gets stuck deep in the cleft of LytF, and the active site is occluded. These results suggest a novel inhibition mechanism of the hacksaw-like structure, which is different from known inhibitor proteins, through interactions around the characteristic loop regions with the active-site cleft of enzymes. PMID:23091053

  12. An Ising spin state explanation for financial asset allocation

    NASA Astrophysics Data System (ADS)

    Horvath, Philip A.; Roos, Kelly R.; Sinha, Amit

    2016-03-01

    We build on the developments in the application of statistical mechanics, notably the identity of the spin degree of freedom in the Ising model, to explain asset price dynamics in financial markets with a representative agent. Specifically, we consider the value of an individual spin to represent the proportional holdings in various assets. We use partial moment arguments to identify asymmetric reactions to information and develop an extension of a plunging and dumping model. This unique identification of the spin is a relaxation of the conventional discrete state limitation on an Ising spin to accommodate a new archetype in Ising model-finance applications wherein spin states may take on continuous values, and may evolve in time continuously, or discretely, depending on the values of the partial moments.

  13. Reply to "Comment on `Canonical-ensemble results for the Ising model with random bonds in two dimensions"'

    NASA Astrophysics Data System (ADS)

    Fernández, Julio F.

    1983-04-01

    In the previous Comment, Binder and Morgenstern use their previous result, 2=c exp(-rijξ) for small systems, plus their hypothesis that ξ and c depend weakly on L, to produce results strongly similar to what I have obtained previously. They thus suggest that my results, contrary to my own conclusion, do not indicate the existence of a critical point in the Edwards-Anderson model in two dimensions. I show here that their claim is not well founded.

  14. Reply to "Comment on `Canonical-ensemble results for the Ising model with random bonds in two dimensions' "

    NASA Astrophysics Data System (ADS)

    Fernández, Julio F.

    1983-05-01

    In the previous Comment, Binder and Morgenstern use their previous result, 2=c exp(-rijξ) for small systems, plus their hypothesis that ξ and c depend weakly on L, to produce results strongly similar to what I have obtained previously. They thus suggest that my results, contrary to my own conclusion, do not indicate the existence of a critical point in the Edwards-Anderson model in two dimensions. I show here that their claim is not well founded.

  15. Three dimensional model of the human mandible.

    PubMed

    Muftić, O; Milcić, D; Saucha, J; Carek, V

    2000-07-01

    A new biomechanical three-dimensional (3D) model for the human mandible is proposed. A simple two-dimensional model cannot explain the biomechanics of the human mandible, where muscular forces through occlusion and condylar surfaces are in a state of dynamical 3D equilibrium. All forces are resolved into components according to a selected coordinate system. The muscular forces, which during clenching act on the jaw, along with the necessary force level for chewing, also act as some kind of stabilizers of the mandibular condyles preventing dislocation and loading of nonarticular tissues.

  16. Critical behavior of two-dimensional models with spatially modulated phases: Analytic results

    NASA Astrophysics Data System (ADS)

    Ruján, P.

    1981-12-01

    The two-dimensional Elliott [or axial next-nearest-neighbor Ising (ANNNI)] model is mapped into an eight-vertex model with direct and staggered fields. With the use of the transfer-matrix approach it is shown that the dual of the ANNNI model belongs to the universality class of the one-dimensional quantum XY model in a staggered field at T=0. The phase structure is investigated by high- and low-temperature expansions of the correlation length and by spin-wave-like approximations valid in first order at low and high temperatures, respectively. The fact that the phase diagram obtained at low temperatures agrees qualitatively with recent results by Villain and Bak and by Coppersmith et al. shows that the paramagnetic phase extends until T=0. The role of the umklapp scattering in determining the critical wave vector in the modulated phase and in stabilizing the <2> antiphase is pointed out. In the eight-vertex representation the critical indices are identified in the floating, massless phase. The dislocations destabilizing this incommensurate phase correspond to the energy operator of the eight-vertex model. Finally, it is argued that the apparent contradiction between the low-temperature results on one hand, and the Monte Carlo simulations and high-temperature-expansion results on the other hand, is probably due to the strong oscillatory behavior of spin-spin correlation functions in the massive paramagnetic region.

  17. 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.

  18. Nature versus nurture: predictability in low-temperature Ising dynamics.

    PubMed

    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(-θ)(h) with θ(h)=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. PMID:24229093

  19. 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.

  20. Nature versus nurture: predictability in low-temperature Ising dynamics.

    PubMed

    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(-θ)(h) with θ(h)=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.

  1. 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.

  2. An Artificial Ising System with Phononic Excitations

    NASA Astrophysics Data System (ADS)

    Ghaffari, Hamed; Griffith, W. Ashley; Benson, Philip; Nasseri, M. H. B.; Young, R. Paul

    Many intractable systems and problems can be reduced to a system of interacting spins. Here, we report mapping collective phononic excitations from different sources of crystal vibrations to spin systems. The phononic excitations in our experiments are due to micro and nano cracking (yielding crackling noises due to lattice distortion). We develop real time mapping of the multi-array senores to a network-space and then mapping the excitation- networks to spin-like systems. We show that new mapped system satisfies the quench (impulsive) characteristics of the Ising model in 2D classical spin systems. In particular, we show that our artificial Ising system transits between two ground states and approaching the critical point accompanies with a very short time frozen regime, inducing formation of domains separated by kinks. For a cubic-test under a true triaxial test (3D case), we map the system to a 6-spin ring under a transversal-driving field where using functional multiplex networks, the vector components of the spin are inferred (i.e., XY model). By visualization of spin patterns of the ring per each event, we demonstrate that ``kinks'' (as defects) proliferate when system approach from above to its critical point. We support our observations with employing recorded acoustic excitations during distortion of crystal lattices in nano-indentation tests on different crystals (silicon and graphite), triaxial loading test on rock (poly-crystal) samples and a true 3D triaxial test.

  3. The Ising Spin Glass in dimension four

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

    The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein et al. (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.

  4. 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.

  5. Taxonomy of particles in Ising spin chains.

    PubMed

    Liu, Dan; Lu, Ping; Müller, Gerhard; Karbach, Michael

    2011-08-01

    The statistical mechanics of particles with shapes on a one-dimensional lattice is investigated in the context of the s=1 Ising chain with uniform nearest-neighbor coupling, quadratic single-site potential, and a magnetic field, which supports four distinct ground states: |↑↓↑↓⋯>, |∘∘⋯>, |↑↑⋯>, |↑∘↑∘⋯>. The complete spectrum is generated from each ground state by particles from a different set of six or seven species. Particles and elements of the pseudovacuum are characterized by motifs (patterns of several consecutive site variables). Particles are floating objects that can be placed into open slots on the lattice. Open slots are recognized as permissible links between motifs. The energy of a particle varies between species but is independent of where it is placed. Placement of one particle changes the open-slot configuration for particles of all species. This statistical interaction is encoded in a generalized Pauli principle, from which the multiplicity of states for a given particle combination is determined and used for the exact statistical mechanical analysis. Particles from all species belong to one of four categories: compacts, hosts, tags, or hybrids. Compacts and hosts find open slots in segments of pseudovacuum. Tags find open slots inside hosts. Hybrids are tags with hosting capability. In the taxonomy of particles proposed here, "species" is indicative of structure and "category" indicative of function. The hosting function splits the Pauli principle into exclusion and accommodation parts. Near phase boundaries, the state of the Ising chain at low temperature is akin to that of miscible or immiscible liquids with particles from one species acting as surfactant molecules.

  6. Arbitrary dimensional Majorana dualities and architectures for topological matter

    NASA Astrophysics Data System (ADS)

    Nussinov, Zohar; Ortiz, Gerardo; Cobanera, Emilio

    2012-08-01

    Motivated by the prospect of attaining Majorana modes at the ends of nanowires, we analyze interacting Majorana systems on general networks and lattices in an arbitrary number of dimensions, and derive universal spin duals. We prove that these interacting Majorana systems, quantum Ising gauge theories, and transverse-field Ising models with annealed bimodal disorder are all dual to one another on general planar graphs. This leads to an interesting connection between heavily disordered annealed Ising systems and uniform Ising theories with nearest-neighbor interactions. As any Dirac fermion (including electronic) operator can be expressed as a linear combination of two Majorana fermion operators, our results further lead to dualities between interacting Dirac fermionic systems on rather general lattices and graphs and corresponding spin systems. Such general complex Majorana architectures (other than those of simple square or other crystalline arrangements) might be of empirical relevance. As these systems display low-dimensional symmetries, they are candidates for realizing topological quantum order. The spin duals allow us to predict the feasibility of various standard transitions as well as spin-glass-type behavior in interacting Majorana fermion or electronic systems. Several systems that can be simulated by arrays of Majorana wires are further introduced and investigated: (1) the XXZ honeycomb compass model (intermediate between the classical Ising model on the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice realization of the model of Xu and Moore for superconducting (p+ip) arrays, and a (3) compass-type two-flavor Hubbard model with both pairing and hopping terms. By the use of our dualities (tantamount to high-dimensional fermionization), we show that all of these systems lie in the three-dimensional Ising universality class. We further discuss how the existence of topological orders and bounds on autocorrelation times can be

  7. On the equivalence between stochastic baker's maps and two-dimensional spin systems

    NASA Astrophysics Data System (ADS)

    Lindgren, K.

    2010-05-01

    We show that there is a class of stochastic bakers transformations that is equivalent to the class of equilibrium solutions of two-dimensional spin systems with finite interaction. The construction is such that the equilibrium distribution of the spin lattice is identical to the invariant measure in the corresponding bakers transformation. We illustrate the equivalence by deriving two stochastic bakers maps representing the Ising model at a temperature above and below the critical temperature, respectively. A calculation of the invariant measure and the free energy in the baker system is then shown to be in agreement with analytic results of the two-dimensional Ising model.

  8. A brief study on coevolution of Ising dynamics

    NASA Astrophysics Data System (ADS)

    Hajra, K. B.; Chandra, A. K.

    2012-01-01

    We consider coevolution of site state and network structures from different initial substrates: a one dimensional Ising chain, a scale free network and network with non-linear degree dependence. The dynamics is governed by a preassigned stability parameter S, and a rewiring factor φ, that determines whether the Ising spin at the chosen site flips or whether the site gets rewired to another site in the system. We have observed the steady state average stability and magnetisation for both kinds of systems to have an idea about the effect of initial network topology. Although the average stability shows almost similar behaviour, the magnetisation depends on the initial condition we start from. Apart from the local dynamics, the global effect on the dynamics has also been studied. These studies show interesting variations in the steady state values of average stability and magnetisation for different values of S and φ, which helps in indicating the gradual change of existing social networks.

  9. Entanglement entropy in a periodically driven quantum Ising ring

    NASA Astrophysics Data System (ADS)

    Apollaro, Tony J. G.; Palma, G. Massimo; Marino, Jamir

    2016-10-01

    We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, h (t ) , of a one-dimensional quantum Ising ring. We consider several realizations of h (t ) , and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After a short-time relaxation, the dynamics of entanglement entropy synchronizes with h (t ) , displaying an oscillatory behavior at the frequency of the driving. Synchronization in the dynamics of entanglement entropy is spoiled by the appearance of quasirevivals which fade out in the thermodynamic limit, and which we interpret using a quasiparticle picture adapted to periodic drivings. We show that the time-averaged entanglement entropy in the synchronized regime obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or a generalized Gibbs ensemble, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model.

  10. Hamiltonian truncation approach to quenches in the Ising field theory

    NASA Astrophysics Data System (ADS)

    Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.

    2016-10-01

    In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.

  11. Three-dimensional pancreas organogenesis models.

    PubMed

    Grapin-Botton, A

    2016-09-01

    A rediscovery of three-dimensional culture has led to the development of organ biogenesis, homeostasis and disease models applicable to human tissues. The so-called organoids that have recently flourished serve as valuable models bridging between cell lines or primary cells grown on the bottom of culture plates and experiments performed in vivo. Though not recapitulating all aspects of organ physiology, the miniature organs generated in a dish are useful models emerging for the pancreas, starting from embryonic progenitors, adult cells, tumour cells and stem cells. This review focusses on the currently available systems and their relevance to the study of the pancreas, of β-cells and of several pancreatic diseases including diabetes. We discuss the expected future developments for studying human pancreas development and function, for developing diabetes models and for producing therapeutic cells. PMID:27615129

  12. System for generating two-dimensional masks from a three-dimensional model using topological analysis

    DOEpatents

    Schiek, Richard

    2006-06-20

    A method of generating two-dimensional masks from a three-dimensional model comprises providing a three-dimensional model representing a micro-electro-mechanical structure for manufacture and a description of process mask requirements, reducing the three-dimensional model to a topological description of unique cross sections, and selecting candidate masks from the unique cross sections and the cross section topology. The method further can comprise reconciling the candidate masks based on the process mask requirements description to produce two-dimensional process masks.

  13. Elucidation of Ground-State Spin Configurations of Ising Models in a Magnetic Field with Frustration on a Diamond Hierarchical Lattice

    NASA Astrophysics Data System (ADS)

    Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki

    2015-10-01

    To study the ground-state spin configuration as a function of magnetic field, the spin configurations at each stage lattice are determined by analyzing recursion equations. The exact calculation of the magnetization curve by Hirose et al. [J. Phys. Soc. Jpn. 83, 074716 (2014)] shows that an infinitely small applied magnetic field on the zero-field classical spin-liquid phase can induce an infinitely small magnetization, which is as if this Ising system has a gapless spectrum. In this study, we reveal that an infinitely small applied field makes a large number of spins flip upwards with the exchange-energy loss remaining finite. This exotic behavior originates from the frustration effect of diamond structures and an inherent long-range nature of hierarchical lattices.

  14. Low dimensional modeling of wall turbulence

    NASA Astrophysics Data System (ADS)

    Aubry, Nadine

    2015-11-01

    In this talk we will review the original low dimensional dynamical model of the wall region of a turbulent boundary layer [Aubry, Holmes, Lumley and Stone, Journal of Fluid Dynamics 192, 1988] and discuss its impact on the field of fluid dynamics. We will also invite a few researchers who would like to make brief comments on the influence Lumley had on their research paths. In collaboration with Philip Holmes, Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ.

  15. Magnetocaloric effect in ferroelectric Ising chain magnet

    NASA Astrophysics Data System (ADS)

    Qi, Yan; Liu, Jia; Yu, Nai-sen; Du, An

    2016-05-01

    We investigate the magnetocaloric effect (MCE) in multiferroic chain system by adopting the elastic Ising-chain model. Based on the transfer-matrix method, the magnetothermal quantities of characterizing MCE behaviors including the entropy, entropy change and adiabatic cooling rate are rigorously determined. Combined with analysis of ground-state, we mainly discuss results in an antiferromagnetic regime associated with ferroelectric transition. Our results show that the entropy change is greatly enhanced near the saturation field as frustration parameter varies in this regime, and accompanied with remarkable inverse MCE, indicating the enormous potential of multiferroic system in low-temperature refrigeration. Meanwhile we also observe a prominent temperature variation in the isoentropy curves close to zero-temperature ferroelectric transition, but this enhancing MCE signal is very sensitive to the thermal fluctuations, and can be strongly suppressed even under a small temperature.

  16. Ising antiferromagnet on the 2-uniform lattices.

    PubMed

    Yu, Unjong

    2016-08-01

    The antiferromagnetic Ising model is investigated on the twenty 2-uniform lattices using the Monte Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which give extensive residual entropy. In the partial spin ice phase, the partial freezing phenomenon appears: A majority of sites are frozen without long-range order, but the other sites are fluctuating even at zero temperature. The spin liquid ground state was not found in the 2-uniform lattices. PMID:27627251

  17. Ising antiferromagnet on the 2-uniform lattices

    NASA Astrophysics Data System (ADS)

    Yu, Unjong

    2016-08-01

    The antiferromagnetic Ising model is investigated on the twenty 2-uniform lattices using the Monte Carlo method based on the Wang-Landau algorithm and the Metropolis algorithm to study the geometric frustration effect systematically. Based on the specific heat, the residual entropy, and the Edwards-Anderson freezing order parameter, the ground states of them were determined. In addition to the long-range-ordered phase and the spin ice phase found in the Archimedean lattices, two more phases were found. The partial long-range order is long-range order with exceptional disordered sites, which give extensive residual entropy. In the partial spin ice phase, the partial freezing phenomenon appears: A majority of sites are frozen without long-range order, but the other sites are fluctuating even at zero temperature. The spin liquid ground state was not found in the 2-uniform lattices.

  18. One-dimensional model of inertial pumping.

    PubMed

    Kornilovitch, Pavel E; Govyadinov, Alexander N; Markel, David P; Torniainen, Erik D

    2013-02-01

    A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location. PMID:23496615

  19. One-dimensional model of inertial pumping.

    PubMed

    Kornilovitch, Pavel E; Govyadinov, Alexander N; Markel, David P; Torniainen, Erik D

    2013-02-01

    A one-dimensional model of inertial pumping is introduced and solved. The pump is driven by a high-pressure vapor bubble generated by a microheater positioned asymmetrically in a microchannel. The bubble is approximated as a short-term impulse delivered to the two fluidic columns inside the channel. Fluid dynamics is described by a Newton-like equation with a variable mass, but without the mass derivative term. Because of smaller inertia, the short column refills the channel faster and accumulates a larger mechanical momentum. After bubble collapse the total fluid momentum is nonzero, resulting in a net flow. Two different versions of the model are analyzed in detail, analytically and numerically. In the symmetrical model, the pressure at the channel-reservoir connection plane is assumed constant, whereas in the asymmetrical model it is reduced by a Bernoulli term. For low and intermediate vapor bubble pressures, both models predict the existence of an optimal microheater location. The predicted net flow in the asymmetrical model is smaller by a factor of about 2. For unphysically large vapor pressures, the asymmetrical model predicts saturation of the effect, while in the symmetrical model net flow increases indefinitely. Pumping is reduced by nonzero viscosity, but to a different degree depending on the microheater location.

  20. Three-dimensional ring current decay model

    NASA Astrophysics Data System (ADS)

    Fok, Mei Ching; Moore, Thomas E.; Kozyra, Janet U.; Ho, George C.; Hamilton, Douglas C.

    1995-06-01

    This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawnside and duskside of the inner magnetosphere spanning the L value range L=2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H+ fluxes at tens of keV, which are always overestimated. A newly invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion diifferential flux. Important features of storm time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (<10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, j0(1+Ayn), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (<30 keV), both drift dispersion and charge exchange are important in determining n. ©American Geophysical 1995

  1. Three-dimensional ring current decay model

    NASA Technical Reports Server (NTRS)

    Fok, Mei-Ching; Moore, Thomas E.; Kozyra, Janet U.; Ho, George C.; Hamilton, Douglas C.

    1995-01-01

    This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawnside and duskside of the inner magnetosphere spanning the L value range L = 2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H(+) fluxes at tens of keV, which are always overestimated. A newly invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion differential flux. Important features of storm time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (less than 10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, J(sub o)(1 + Ay(sup n)), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (less than 30 keV), both drift dispersion and charge exchange are important in determining n.

  2. Critical behavior of a triangular lattice Ising AF/FM bilayer

    NASA Astrophysics Data System (ADS)

    Žukovič, M.; Bobák, A.

    2016-03-01

    We study a bilayer Ising spin system consisting of antiferromagnetic (AF) and ferromagnetic (FM) triangular planes, coupled by ferromagnetic exchange interaction, by standard Monte Carlo and parallel tempering methods. The AF/FM bilayer is found to display the critical behavior completely different from both the single FM and AF constituents as well as the FM/FM and AF/AF bilayers. Namely, by finite-size scaling (FSS) analysis we identify at the same temperature a standard Ising transition from the paramagnetic to FM state in the FM plane that induces a ferrimagnetic state with a finite net magnetic moment in the AF plane. At lower temperatures there is another phase transition, that takes place only in the AF plane, to different ferrimagnetic state with spins on two sublattices pointing parallel and on one sublattice antiparallel to the spins on the FM plane. FSS indicates that the corresponding critical exponents are close to the two-dimensional three-state ferromagnetic Potts model values.

  3. Vlasov multi-dimensional model dispersion relation

    SciTech Connect

    Lushnikov, Pavel M.; Rose, Harvey A.; Silantyev, Denis A.; Vladimirova, Natalia

    2014-07-15

    A hybrid model of the Vlasov equation in multiple spatial dimension D > 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θ{sup N}, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.

  4. Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

    NASA Astrophysics Data System (ADS)

    Song, Huimin

    In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and

  5. The ISEE 1 and 2 Medium Energy Particles Experiment

    NASA Technical Reports Server (NTRS)

    Williams, D. J.; Fritz, T. A.; Keppler, E.; Wilken, B.; Wibberenz, G.

    1978-01-01

    The Medium Energy Particles Experiment (MEPE) on board ISEE 1 and 2 consists of the WIM instrument on ISEE 1 and the KED instrument on ISEE 2. Both instruments employ solid-state detectors and magnetic analysis to measure the angular, energy, and intensity distributions of protons (ions) above 24 keV and electrons above 20 keV. The WIM instrument also includes a composition measurement employing Delta E-by-E and time-of-flight techniques. Three-parameter analysis is performed above 250 keV/nucleon, and single parameter analysis is performed above 125 keV/nucleon for helium through oxygen. Three-dimensional angular distributions are obtained through the use of a scan platform in the WIM instrument and multiple detector heads in the KED instrument. A variety of operational modes are used to optimize data collection from both instruments. Resolutions up to 128 channels in energy, 192 samples over the unit sphere in angle, and 0.095 sec in time are available.

  6. Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models

    SciTech Connect

    Enciso, Alberto; Finkel, Federico; Gonzalez-Lopez, Artemio

    2012-11-15

    We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A{sub N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these models for an arbitrary finite number of spins. We then show that these chains are equivalent to a suitable inhomogeneous classical Ising model in a spatially dependent magnetic field, generalizing the results of Basu-Mallick et al. for the zero magnetic field case. Using the standard transfer matrix approach, we are able to compute in closed form the free energy per site in the thermodynamic limit. We perform a detailed analysis of the chains' thermodynamics in a unified way, with special emphasis on the zero field and zero temperature limits. Finally, we provide a novel interpretation of the thermodynamic quantities of spin chains of Haldane-Shastry type as weighted averages of the analogous quantities over an ensemble of classical Ising models. - Highlights: Black-Right-Pointing-Pointer Partition function of spin chains of Haldane-Shastry type in magnetic field. Black-Right-Pointing-Pointer Equivalence to classical inhomogeneous Ising models. Black-Right-Pointing-Pointer Free energy per site, other thermodynamic quantities in thermodynamic limit. Black-Right-Pointing-Pointer Zero field, zero temperature limits. Black-Right-Pointing-Pointer Thermodynamic equivalence with ensemble of classical Ising models.

  7. Exact results of a mixed spin-1/2 and spin- S Ising model on a bathroom tile (4-8) lattice: Effect of uniaxial single-ion anisotropy

    NASA Astrophysics Data System (ADS)

    Strečka, Jozef

    2006-02-01

    Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin- S ( S⩾1) Ising model on a bathroom tile (4-8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams established for several values of the quantum spin number S. It is shown that the mixed-spin bathroom tile lattice exhibits very similar phase boundaries as the mixed-spin honeycomb lattice whose critical points are merely slightly enhanced with respect to the former ones. The influence of uniaxial single-ion anisotropy upon the total magnetization vs. temperature dependence is particularly investigated as well.

  8. Incorporating 3-dimensional models in online articles

    PubMed Central

    Cevidanes, Lucia H. S.; Ruellasa, Antonio C. O.; Jomier, Julien; Nguyen, Tung; Pieper, Steve; Budin, Francois; Styner, Martin; Paniagua, Beatriz

    2015-01-01

    Introduction The aims of this article were to introduce the capability to view and interact with 3-dimensional (3D) surface models in online publications, and to describe how to prepare surface models for such online 3D visualizations. Methods Three-dimensional image analysis methods include image acquisition, construction of surface models, registration in a common coordinate system, visualization of overlays, and quantification of changes. Cone-beam computed tomography scans were acquired as volumetric images that can be visualized as 3D projected images or used to construct polygonal meshes or surfaces of specific anatomic structures of interest. The anatomic structures of interest in the scans can be labeled with color (3D volumetric label maps), and then the scans are registered in a common coordinate system using a target region as the reference. The registered 3D volumetric label maps can be saved in .obj, .ply, .stl, or .vtk file formats and used for overlays, quantification of differences in each of the 3 planes of space, or color-coded graphic displays of 3D surface distances. Results All registered 3D surface models in this study were saved in .vtk file format and loaded in the Elsevier 3D viewer. In this study, we describe possible ways to visualize the surface models constructed from cone-beam computed tomography images using 2D and 3D figures. The 3D surface models are available in the article’s online version for viewing and downloading using the reader’s software of choice. These 3D graphic displays are represented in the print version as 2D snapshots. Overlays and color-coded distance maps can be displayed using the reader’s software of choice, allowing graphic assessment of the location and direction of changes or morphologic differences relative to the structure of reference. The interpretation of 3D overlays and quantitative color-coded maps requires basic knowledge of 3D image analysis. Conclusions When submitting manuscripts, authors can

  9. High dimensional decision dilemmas in climate models

    NASA Astrophysics Data System (ADS)

    Bracco, A.; Neelin, J. D.; Luo, H.; McWilliams, J. C.; Meyerson, J. E.

    2013-10-01

    An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Building upon on the smoothness of the response of an atmospheric circulation model (AGCM) to changes of four adjustable parameters, Neelin et al. (2010) used a quadratic metamodel to objectively calibrate the AGCM. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g., how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions.

  10. High dimensional decision dilemmas in climate models

    NASA Astrophysics Data System (ADS)

    Bracco, A.; Neelin, J. D.; Luo, H.; McWilliams, J. C.; Meyerson, J. E.

    2013-05-01

    An important source of uncertainty in climate models is linked to the calibration of model parameters. Interest in systematic and automated parameter optimization procedures stems from the desire to improve the model climatology and to quantify the average sensitivity associated with potential changes in the climate system. Neelin et al. (2010) used a quadratic metamodel to objectively calibrate an atmospheric circulation model (AGCM) around four adjustable parameters. The metamodel accurately estimates global spatial averages of common fields of climatic interest, from precipitation, to low and high level winds, from temperature at various levels to sea level pressure and geopotential height, while providing a computationally cheap strategy to explore the influence of parameter settings. Here, guided by the metamodel, the ambiguities or dilemmas related to the decision making process in relation to model sensitivity and optimization are examined. Simulations of current climate are subject to considerable regional-scale biases. Those biases may vary substantially depending on the climate variable considered, and/or on the performance metric adopted. Common dilemmas are associated with model revisions yielding improvement in one field or regional pattern or season, but degradation in another, or improvement in the model climatology but degradation in the interannual variability representation. Challenges are posed to the modeler by the high dimensionality of the model output fields and by the large number of adjustable parameters. The use of the metamodel in the optimization strategy helps visualize trade-offs at a regional level, e.g. how mismatches between sensitivity and error spatial fields yield regional errors under minimization of global objective functions.

  11. A three-dimensional human walking model

    NASA Astrophysics Data System (ADS)

    Yang, Q. S.; Qin, J. W.; Law, S. S.

    2015-11-01

    A three-dimensional human bipedal walking model with compliant legs is presented in this paper. The legs are modeled with time-variant dampers, and the model is able to characterize the gait pattern of an individual using a minimal set of parameters. Feedback control, for both the forward and lateral movements, is implemented to regulate the walking performance of the pedestrian. The model provides an improvement over classic invert pendulum models. Numerical studies were undertaken to investigate the effects of leg stiffness and attack angle. Simulation results show that when walking at a given speed, increasing the leg stiffness with a constant attack angle results in a longer step length, a higher step frequency, a faster walking speed and an increase in both the peak vertical and lateral ground reaction forces. Increasing the attack angle with a constant leg stiffness results in a higher step frequency, a decrease in the step length, an increase in the total energy of the system and a decrease in both the peak vertical and lateral ground reaction forces.

  12. Describing high-dimensional dynamics with low-dimensional piecewise affine models: applications to renewable energy.

    PubMed

    Hirata, Yoshito; Aihara, Kazuyuki

    2012-06-01

    We introduce a low-dimensional description for a high-dimensional system, which is a piecewise affine model whose state space is divided by permutations. We show that the proposed model tends to predict wind speeds and photovoltaic outputs for the time scales from seconds to 100 s better than by global affine models. In addition, computations using the piecewise affine model are much faster than those of usual nonlinear models such as radial basis function models.

  13. 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.

  14. Three-dimensional model of lignin structure

    SciTech Connect

    Jurasek, L.

    1995-12-01

    An attempt to build a three-dimensional model of lignin structure using a computer program is described. The program simulates the biosynthesis of spruce lignin by allowing coniferyl alcohol subunits to be added randomly by six different types of linkages, assumed to be most common. The simulated biosynthesis starts from a number of seed points within restricted space, corresponding to 50 mM initial concentration of coniferyl alcohol. Rules of three-dimensional packing of the subunits within the lignin macro-molecule are observed during the simulated biosynthetic process. Branched oligomeric structures thus generated form crosslinks at those positions where the chains grow close enough to form a link. Inter-chain crosslinking usually joins the oligomers into one macromolecule. Intra-chain crosslinks are also formed and result in closed loops. Typically, a macromolecule with molecular weight of approx. 2 x 105 is formed, with internal density of 1.35g/cm3. Various characteristics of the internal structure, such as branching, crosslinking, bond frequencies, and chain length distribution are described. Breakdown of the polymer was also simulated and the effect of closed loops on the weight average molecular weight is shown. The effect of the shape of the biosynthetic space on the degree of crosslinking is discussed and predictions of the overall molecular shape of lignin particles are made.

  15. A Standardized Generalized Dimensionality Discrepancy Measure and a Standardized Model-Based Covariance for Dimensionality Assessment for Multidimensional Models

    ERIC Educational Resources Information Center

    Levy, Roy; Xu, Yuning; Yel, Nedim; Svetina, Dubravka

    2015-01-01

    The standardized generalized dimensionality discrepancy measure and the standardized model-based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence.…

  16. Multiscale modeling of three-dimensional genome

    NASA Astrophysics Data System (ADS)

    Zhang, Bin; Wolynes, Peter

    The genome, the blueprint of life, contains nearly all the information needed to build and maintain an entire organism. A comprehensive understanding of the genome is of paramount interest to human health and will advance progress in many areas, including life sciences, medicine, and biotechnology. The overarching goal of my research is to understand the structure-dynamics-function relationships of the human genome. In this talk, I will be presenting our efforts in moving towards that goal, with a particular emphasis on studying the three-dimensional organization, the structure of the genome with multi-scale approaches. Specifically, I will discuss the reconstruction of genome structures at both interphase and metaphase by making use of data from chromosome conformation capture experiments. Computationally modeling of chromatin fiber at atomistic level from first principles will also be presented as our effort for studying the genome structure from bottom up.

  17. Ising nematic quantum critical point in a metal: a Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Lederer, Samuel

    The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic metal is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to 24 × 24 sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP. With Yoni Schattner, Steven A. Kivelson, and Erez Berg.

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

    DOE PAGES

    Liu, Guangkun; Kaushal, Nitin; Liu, Shaozhi; Bishop, Christopher B.; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio R.

    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

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

    NASA Astrophysics Data System (ADS)

    Liu, Guangkun; Kaushal, Nitin; Li, Shaozhi; Bishop, Christopher B.; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio

    2016-06-01

    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), 10.1103/PhysRevLett.112.106405]. In this publication 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. We also study a simplified version of the 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. 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.

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

    PubMed

    Liu, Guangkun; Kaushal, Nitin; Li, Shaozhi; Bishop, Christopher B; Wang, Yan; Johnston, Steve; Alvarez, Gonzalo; Moreo, Adriana; Dagotto, Elbio

    2016-06-01

    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)PRLTAO0031-900710.1103/PhysRevLett.112.106405]. In this publication 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. We also study a simplified version of the 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. 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. PMID:27415393

  1. Three-dimensional modeling of tsunami waves

    SciTech Connect

    Mader, C.L.

    1985-01-01

    Two- and three-dimensional, time-dependent, nonlinear, incompressible, viscous flow calculations of realistic models of tsunami wave formation and run up have been performed using the Los Alamos-developed SOLA-3D code. The results of the SOLA calculations are compared with shallow-water, long-wave calculations for the same problems using the SWAN code. Tsunami wave formation by a continental slope subsidence has been examined using the two numerical models. The SOLA waves were slower than the SWAN waves and the interaction with the shoreline was more complicated for the SOLA waves. In the SOLA calculation, the first wave was generated by the cavity being filled along the shoreline close to the source of motion. The second wave was generated by the cavity being filled from the deep water end. The two waves interacted along the shoreline resulting in the second wave being the largest wave with a velocity greater than the first wave. The second wave overtook the first wave at later times and greater distances from the source. In the SWAN calculation, the second wave was smaller than the first wave. 6 refs.

  2. A one dimensional model of population growth

    NASA Astrophysics Data System (ADS)

    Ribeiro, Fabiano L.; Ribeiro, Kayo N.

    2015-09-01

    In this work, a one dimensional population growth model is proposed. The model, based on the cooperative and competitive individual-individual distance-dependent interaction, allows us to get a full analytical solution. With this analytical approach, it was possible to investigate the dynamics of the population according to some parameters, as intrinsic growth rate, strength of the interaction between individuals, and the distance-dependent interaction. As a consequence of the individuals' interaction, a rich phase diagram to which the population has access was observed. The phases observed are: convergence to carrying capacity, exponential growth, divergence at finite time, and extinction. Moreover, it was also observed that some phases are strictly dependent on the initial condition. For instance, in the cooperative regime with negative intrinsic growth rate, the population can diverge or become extinct according to the initial population size. The phases accessible to the population can be seen as a macroscopic behavior which emerges from the interaction among the individuals (the microscopic level).

  3. Phase diagrams of the Ising-Heisenberg chain with S = 1/2 triangular XXZ clusters

    SciTech Connect

    Ohanyan, V.

    2010-03-15

    The one-dimensional spin system consisted of triangular S = 1/2 XXZ Heisenberg clusters alternating with single Ising spins is considered. Partition function of the system is calculated exactly within the transfer-matrix formalism. T = 0 ground state phase diagrams, corresponding to different regions of the values of system parameters, are obtained.

  4. Ising Quantum Hall Ferromagnetism in AlAs Quantum Wells.

    NASA Astrophysics Data System (ADS)

    de Poortere, Etienne

    2002-03-01

    Though quantum Hall ferromagnetic transitions in two-dimensional (2D) systems are observed in several materials, such transitions in AlAs 2D electrons offer a unique combination of two remarkable properties: (1) the resistance of the carrier system increases sharply at the transition, and (2) these resistance spikes are hysteretic at low temperatures [1]. We have been able to uncover these properties thanks to recent improvements in the quality of our AlAs samples [2], which now attain a mobility as high as 31 m^2/Vs at a density 5 × 10^11 cm-2. These transport phenomena at Ising transitions result in part from the electronic properties of AlAs, which favor a strong competition between exchange, cyclotron and Zeeman energies. Indeed, 2D electrons in AlAs have a high and anisotropic effective band mass comparable to that of Si, and a band g-factor close to 2. In addition, high-density AlAs 2D electrons occupy two X-point valleys of the Brillouin zone, allowing for inter-valley Ising transitions. In this talk we present results from our study of Ising transitions in AlAs 2D electrons. We observe that the hysteretic resistance of a given transition depends sensitively on the occupation of the two levels involved in the transition, increasing in amplitude as these levels are depleted. We also analyze the spike temperature dependence, which shows that unlike the nearby quantum Hall resistance minima, the resistance spikes themselves are not activated. Other parameters are also varied, such as total carrier density and transverse electric field in the AlAs quantum well. A Hartree-Fock picture of these Ising transitions has been drawn, involving magnetic domains and increased scattering at the domain boundaries [3]. Nevertheless, many of the measured dependencies of the Ising transition resistance spikes are not yet qualitatively understood, forming thus a jigsaw puzzle of many parts. [1] E. P. De Poortere et al., Science 290, 1546 (2000). [2] E. P. De Poortere et al

  5. Applications of ISES for meteorology

    NASA Technical Reports Server (NTRS)

    Try, Paul D.

    1990-01-01

    The results are summarized from an initial assessment of the potential real-time meteorological requirements for the data from Eos systems. Eos research scientists associated with facility instruments, investigator instruments, and interdisciplinary groups with data related to meteorological support were contacted, along with those from the normal operational user and technique development groups. Two types of activities indicated the greatest need for real-time Eos data: technology transfer groups (e.g., NOAA's Forecasting System Laboratory and the DOD development laboratories), and field testing groups with airborne operations. A special concern was expressed by several non-U.S. participants who desire a direct downlink to be sure of rapid receipt of the data for their area of interest. Several potential experiments or demonstrations are recommended for ISES which include support for hurricane/typhoon forecasting, space shuttle reentry, severe weather forecasting (using microphysical cloud classification techniques), field testing, and quick reaction of instrumented aircraft to measure such events as polar stratospheric clouds and volcanic eruptions.

  6. 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.

  7. Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models

    NASA Technical Reports Server (NTRS)

    Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.

    2004-01-01

    One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.

  8. Ising spin glasses: Corrections to finite size scaling, freezing temperatures, and critical exponents

    NASA Astrophysics Data System (ADS)

    Mari, P. O.; Campbell, I. A.

    1999-03-01

    We compare simulation data from different sources on two canonical three-dimensional Ising spin glasses (ISGs): the binomial +/-J near-neighbor interaction ISG and the Gaussian interaction ISG. We allow for the possibility of corrections to finite size scaling and estimate the correction exponent w. Consistent estimates for the critical temperatures Tg and for the critical exponents for each system are obtained. The data strongly indicate that critical exponents in the two systems are significantly different from each other. These results thus confirm a breakdown of standard universality rules in Ising spin glasses.

  9. Quantum algorithm for an additive approximation of Ising partition functions

    NASA Astrophysics Data System (ADS)

    Matsuo, Akira; Fujii, Keisuke; Imoto, Nobuyuki

    2014-08-01

    We investigate quantum-computational complexity of calculating partition functions of Ising models. We construct a quantum algorithm for an additive approximation of Ising partition functions on square lattices. To this end, we utilize the overlap mapping developed by M. Van den Nest, W. Dür, and H. J. Briegel [Phys. Rev. Lett. 98, 117207 (2007), 10.1103/PhysRevLett.98.117207] and its interpretation through measurement-based quantum computation (MBQC). We specify an algorithmic domain, on which the proposed algorithm works, and an approximation scale, which determines the accuracy of the approximation. We show that the proposed algorithm performs a nontrivial task, which would be intractable on any classical computer, by showing that the problem that is solvable by the proposed quantum algorithm is BQP-complete. In the construction of the BQP-complete problem coupling strengths and magnetic fields take complex values. However, the Ising models that are of central interest in statistical physics and computer science consist of real coupling strengths and magnetic fields. Thus we extend the algorithmic domain of the proposed algorithm to such a real physical parameter region and calculate the approximation scale explicitly. We found that the overlap mapping and its MBQC interpretation improve the approximation scale exponentially compared to a straightforward constant-depth quantum algorithm. On the other hand, the proposed quantum algorithm also provides partial evidence that there exist no efficient classical algorithm for a multiplicative approximation of the Ising partition functions even on the square lattice. This result supports the observation that the proposed quantum algorithm also performs a nontrivial task in the physical parameter region.

  10. Ground-state phase diagram of the one-dimensional Hubbard model with an alternating chemical potential

    NASA Astrophysics Data System (ADS)

    Otsuka, Hiromi; Nakamura, Masaaki

    2005-04-01

    We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential—a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidence to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.

  11. Three-Dimensional Lithium-Ion Battery Model (Presentation)

    SciTech Connect

    Kim, G. H.; Smith, K.

    2008-05-01

    Nonuniform battery physics can cause unexpected performance and life degradations in lithium-ion batteries; a three-dimensional cell performance model was developed by integrating an electrode-scale submodel using a multiscale modeling scheme.

  12. Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

    NASA Astrophysics Data System (ADS)

    Tsuchiizu, M.; Furusaki, A.

    2004-01-01

    We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for U≈2V in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential Δ or bond alternation δ. Although the alternating site potential Δ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation δ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with δ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of Δ or δ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.

  13. Statistical Properties and Multifractal Behaviors of Market Returns by Ising Dynamic Systems

    NASA Astrophysics Data System (ADS)

    Fang, Wen; Wang, Jun

    An interacting-agent model of speculative activity explaining price formation in financial markets is considered in the present paper, which based on the stochastic Ising model and the mean field theory. The model describes the interaction strength among the agents as well as an external field, and the corresponding random logarithmic price return process is investigated. According to the empirical research of the model, the time series formed by this Ising model exhibits the bursting typical of volatility clustering, the fat-tail phenomenon, the power-law distribution tails and the long-time memory. The statistical properties of the returns of Hushen 300 Index, Shanghai Stock Exchange (SSE) Composite Index and Shenzhen Stock Exchange (SZSE) Component Index are also studied for comparison between the real time series and the simulated ones. Further, the multifractal detrended fluctuation analysis is applied to investigate the time series returns simulated by Ising model have the distribution multifractality as well as the correlation multifractality.

  14. Roaming form factors for the tricritical to critical Ising flow

    NASA Astrophysics Data System (ADS)

    Horváth, D. X.; Dorey, P. E.; Takács, G.

    2016-07-01

    We study the massless flows described by the staircase model introduced by Al.B. Zamolodchikov through the analytic continuation of the sinh-Gordon S-matrix, focusing on the renormalisation group flow from the tricritical to the critical Ising model. We show that the properly defined roaming limits of certain sinh-Gordon form factors are identical to the form factors of the order and disorder operators for the massless flow. As a by-product, we also construct form factors for a semi-local field in the sinh-Gordon model, which can be associated with the twist field in the ultraviolet limiting free massless bosonic theory.

  15. 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.

  16. Finite-size critical scaling in Ising spin glasses in the mean-field regime

    NASA Astrophysics Data System (ADS)

    Aspelmeier, T.; Katzgraber, Helmut G.; Larson, Derek; Moore, M. A.; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

  17. Finite-size critical scaling in Ising spin glasses in the mean-field regime.

    PubMed

    Aspelmeier, T; Katzgraber, Helmut G; Larson, Derek; Moore, M A; Wittmann, Matthew; Yeo, Joonhyun

    2016-03-01

    We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent. PMID:27078308

  18. Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

    PubMed

    Schaffenberger, Werner; Hanslmeier, Arnold

    2002-10-01

    We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

  19. A Five Dimensional Model for Educating the Net Generation

    ERIC Educational Resources Information Center

    Beyers, Ronald Noel

    2009-01-01

    This paper proposes a multi-dimensional concept model of an ICT enabled classroom to highlight potential similarities and differences between where teachers perceive themselves relative to their learners. Some teachers and learners may be at the two dimensional text-book level, while others are operating in at a globalization level. Being armed…

  20. Mean-field theory for the inverse Ising problem at low temperatures.

    PubMed

    Nguyen, H Chau; Berg, Johannes

    2012-08-01

    The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetizations and correlations), mean-field approximations are often used, allowing the determination of model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here, we show how clustering spin configurations can approximate these thermodynamic states and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

  1. Three-dimensional micro-diffraction modeling.

    PubMed

    Castañeda, Román

    2014-03-20

    Squared elementary cells with correlated radiant point sources are presented as basic structures for characterizing the propagation of the field emitted by two-dimensional planar sources of any shape and in arbitrary state of spatial coherence. The field is transported on a finite expansion of nonparaxial modes, whose propagation in the micro-diffraction domain is discussed under both the diffraction and the interference conditions.

  2. Dynamic colloidal assembly pathways via low dimensional models

    NASA Astrophysics Data System (ADS)

    Yang, Yuguang; Thyagarajan, Raghuram; Ford, David M.; Bevan, Michael A.

    2016-05-01

    Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterized by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.

  3. Model of a Negatively Curved Two-Dimensional Space.

    ERIC Educational Resources Information Center

    Eckroth, Charles A.

    1995-01-01

    Describes the construction of models of two-dimensional surfaces with negative curvature that are used to illustrate differences in the triangle sum rule for the various Big Bang Theories of the universe. (JRH)

  4. ISEE/ICE plasma wave data analysis

    NASA Technical Reports Server (NTRS)

    Greenstadt, E. W.

    1989-01-01

    The work performed for the period 1 Jan. 1985 to 30 Oct. 1989 is presented. The objective was to provide reduction and analysis of data from a scientific instrument designed to study solar wind and plasma wave phenomena on the International Sun Earth Explorer 3 (ISEE-3)/International Cometary Explorer (ICE) missions.

  5. Two-Dimensional Intercomparison of Stratospheric Models

    NASA Technical Reports Server (NTRS)

    Jackman, Charles H. (Editor); Seals, Robert K., Jr. (Editor); Prather, Michael J. (Editor)

    1989-01-01

    A detailed record is provided for the examination of fundamental differences in photochemistry and transport among atmospheric models. The results of 16 different modeling groups are presented for several model experiments.

  6. Three Dimensional Vapor Intrusion Modeling: Model Validation and Uncertainty Analysis

    NASA Astrophysics Data System (ADS)

    Akbariyeh, S.; Patterson, B.; Rakoczy, A.; Li, Y.

    2013-12-01

    Volatile organic chemicals (VOCs), such as chlorinated solvents and petroleum hydrocarbons, are prevalent groundwater contaminants due to their improper disposal and accidental spillage. In addition to contaminating groundwater, VOCs may partition into the overlying vadose zone and enter buildings through gaps and cracks in foundation slabs or basement walls, a process termed vapor intrusion. Vapor intrusion of VOCs has been recognized as a detrimental source for human exposures to potential carcinogenic or toxic compounds. The simulation of vapor intrusion from a subsurface source has been the focus of many studies to better understand the process and guide field investigation. While multiple analytical and numerical models were developed to simulate the vapor intrusion process, detailed validation of these models against well controlled experiments is still lacking, due to the complexity and uncertainties associated with site characterization and soil gas flux and indoor air concentration measurement. In this work, we present an effort to validate a three-dimensional vapor intrusion model based on a well-controlled experimental quantification of the vapor intrusion pathways into a slab-on-ground building under varying environmental conditions. Finally, a probabilistic approach based on Monte Carlo simulations is implemented to determine the probability distribution of indoor air concentration based on the most uncertain input parameters.

  7. 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 .

  8. The Long Decay Model of One-Dimensional Projectile Motion

    ERIC Educational Resources Information Center

    Lattery, Mark Joseph

    2008-01-01

    This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo ("in De Motu") and by contemporary students. Implications for instruction are…

  9. SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems

    NASA Astrophysics Data System (ADS)

    Ciaramella, G.; Borzì, A.

    2015-05-01

    The modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-1/2 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov-Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank-Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem.

  10. 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

  11. Multiscale modeling of two-dimensional contacts.

    PubMed

    Luan, B Q; Hyun, S; Molinari, J F; Bernstein, N; Robbins, Mark O

    2006-10-01

    A hybrid simulation method is introduced and used to study two-dimensional single-asperity and multi-asperity contacts both quasistatically and dynamically. The method combines an atomistic treatment of the interfacial region with a finite-element method description of subsurface deformations. The dynamics in the two regions are coupled through displacement boundary conditions applied at the outer edges of an overlap region. The two solutions are followed concurrently but with different time resolution. The method is benchmarked against full atomistic simulations. Accurate results are obtained for contact areas, pressures, and static and dynamic friction forces. The time saving depends on the fraction of the system treated atomistically and is already more than a factor of 20 for the relatively small systems considered here.

  12. Nonminimal universal extra dimensional model confronts Bs→μ+μ-

    NASA Astrophysics Data System (ADS)

    Datta, Anindya; Shaw, Avirup

    2016-03-01

    The addition of boundary localized kinetic and Yukawa terms to the action of a five-dimensional Standard Model would nontrivially modify the Kaluza-Klein spectra and some of the interactions among the Kaluza-Klein excitations compared to the minimal version of this model, in which these boundary terms are not present. In the minimal version of this framework, known as the universal extra dimensional model, special assumptions are made about these unknown, beyond the cutoff contributions to restrict the number of unknown parameters of the theory to be minimum. We estimate the contribution of Kaluza-Klein modes to the branching ratios of Bs (d )→μ+μ- in the framework of the nonminimal universal extra dimensional model, at one-loop level. The results have been compared to the experimental data to constrain the parameters of this model. From the measured decay branching ratio of Bs→μ+μ- (depending on the values of boundary localized parameters), the lower limit on R-1 can be as high as 800 GeV. We have briefly reviewed the bounds on nonminimal universal extra dimensional parameter space coming from electroweak precision observables. The present analysis (Bs→μ+μ-) has ruled out new regions of parameter space in comparison to the analysis of electroweak data. We have revisited the bound on R-1 in the universal extra dimensional model, which came out to be 454 GeV. This limit on R-1 in the universal extra dimensional framework is not as competitive as the limits derived from the consideration of relic density or Standard Model Higgs boson production and decay to W+W-. Unfortunately, the Bd→μ+μ- decay branching ratio would not set any significant limit on R-1 in a minimal or nonminimal universal extra dimensional model.

  13. Finite-temperature scaling at the quantum critical point of the Ising chain in a transverse field

    NASA Astrophysics Data System (ADS)

    Haelg, Manuel; Huvonen, Dan; Guidi, Tatiana; Quintero-Castro, Diana Lucia; Boehm, Martin; Regnault, Louis-Pierre; Zheludev, Andrey

    2015-03-01

    Inelastic neutron scattering is used to study the finite-temperature scaling behavior of spin correlations at the quantum critical point in an experimental realization of the one-dimensional Ising model in a transverse field. The target compound is the well-characterized, anisotropic and bond-alternating Heisenberg spin-1 chain material NTENP. The validity and the limitations of the dynamic structure factor scaling are tested, discussed and compared to theoretical predictions. For this purpose neutron data have been collected on the three-axes spectrometers IN14 at ILL and FLEXX at HZB as well as on the time of flight multi-chopper spectrometer LET at ISIS. In addition to the general statement about quantum criticality and universality, present study also reveals new insight into the properties of the spin chain compound NTENP in particular.

  14. Response characteristics of a low-dimensional model neuron.

    PubMed

    Cartling, B

    1996-11-15

    It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidations of neurocomputational mechanisms, and applications to large-scale systems.

  15. A two-dimensional dam-break flood plain model

    USGS Publications Warehouse

    Hromadka, T.V., II; Berenbrock, C.E.; Freckleton, J.R.; Guymon, G.L.

    1985-01-01

    A simple two-dimensional dam-break model is developed for flood plain study purposes. Both a finite difference grid and an irregular triangle element integrated finite difference formulation are presented. The governing flow equations are approximately solved as a diffusion model coupled to the equation of continuity. Application of the model to a hypothetical dam-break study indicates that the approach can be used to predict a two-dimensional dam-break flood plain over a broad, flat plain more accurately than a one-dimensional model, especially when the flow can break-out of the main channel and then return to the channel at other downstream reaches. ?? 1985.

  16. Multi-Scale Multi-Dimensional Ion Battery Performance Model

    2007-05-07

    The Multi-Scale Multi-Dimensional (MSMD) Lithium Ion Battery Model allows for computer prediction and engineering optimization of thermal, electrical, and electrochemical performance of lithium ion cells with realistic geometries. The model introduces separate simulation domains for different scale physics, achieving much higher computational efficiency compared to the single domain approach. It solves a one dimensional electrochemistry model in a micro sub-grid system, and captures the impacts of macro-scale battery design factors on cell performance and materialmore » usage by solving cell-level electron and heat transports in a macro grid system.« less

  17. One-dimensional hydrodynamic model generating a turbulent cascade.

    PubMed

    Matsumoto, Takeshi; Sakajo, Takashi

    2016-05-01

    As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure. PMID:27300972

  18. Quantum Walks on Two Kinds of Two-Dimensional Models

    NASA Astrophysics Data System (ADS)

    Li, Dan; Mc Gettrick, Michael; Zhang, Wei-Wei; Zhang, Ke-Jia

    2015-08-01

    In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum walks on these two models. Also, we study its dependence on the initial state, size of the model. At the same time, we compare the quantum walk and classical walk on these two models to discuss the difference of quantum walk and classical walk.

  19. Recent developments in three-dimensional numerical estuarine models

    USGS Publications Warehouse

    Cheng, Ralph T.; Smith, Peter E.; Casulli, Vincenzo

    1993-01-01

    For a fixed cost, computing power increases 5 to 10 times every five years. The readily available computing resources have inspired new modal formulations and innovative model applications. Significant progress has been advanced in three-dimensional numerical estuarine modeling within the past three or four years. This paper attempts to review and summarize properties of new 3-D estuarine hydrodynamic models. The emphasis of the review is placed on the formulation, numerical methods. The emphasis of the review is placed on the formulation, numerical methods, spatial and temporal resolution, computational efficiency, and turbulence closure of new models. Recent research has provided guidelines for the proper use of 3-D models involving in the σ-transformation. Other models resort to a fixed level discretization in the vertical. The semi-implicit treatment in time-stepping models appears to have gained momentum. Future research in three-dimensional numerical modeling remains to be on computational efficiency and turbulent closure.

  20. Low-dimensional supersymmetric lattice models

    SciTech Connect

    Bergner, G. Kaestner, T. Uhlmann, S. Wipf, A.

    2008-04-15

    We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In one dimension, our simulations show that a model with the Wilson derivative and the Stratonovich prescription for this discretization leads to far better results at finite lattice spacing than other models with Wilson fermions considered in the literature. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order O(a{sup 2}). Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.

  1. Large field inflation models from higher-dimensional gauge theories

    NASA Astrophysics Data System (ADS)

    Furuuchi, Kazuyuki; Koyama, Yoji

    2015-02-01

    Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.

  2. Large field inflation models from higher-dimensional gauge theories

    SciTech Connect

    Furuuchi, Kazuyuki; Koyama, Yoji

    2015-02-23

    Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.

  3. High spacecraft potentials on ISEE-1 in sunlight

    NASA Technical Reports Server (NTRS)

    Whipple, E. C., Jr.; Olsen, R. C.

    1987-01-01

    Data from two electric field experiments and from the plasma composition experiment on ISEE-1 show that the spacecraft charged to close to -70 V in sunlight at about 0700 UT on March 17, 1978. Data from the electron spectrometer experiment show that there was a potential barrier of some -10 to -20 V about the spacecraft during this event. The potential barrier was effective in turning back emitted photoelectrons to the spacecraft. Potential barriers can be formed by differential charging on the spacecraft or by the presence of space charge. The stringent electrostatic cleanliness specifications imposed on ISEE made the presence of differential charging seem unlikely, if these precautions were effective. Modeling of the event to determine if the barrier was produced by the presence of space charge suggested that this could not explain the observed barrier. The angular shape of the distribution could be successfully modeled as a product of differential charging on the solar arrays. This implies that the conductive coating was not completely effective in preventing differential charging, and that differential charging did occur.

  4. Underwater striling engine design with modified one-dimensional model

    NASA Astrophysics Data System (ADS)

    Li, Daijin; Qin, Kan; Luo, Kai

    2015-05-01

    Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.

  5. Underwater striling engine design with modified one-dimensional model

    NASA Astrophysics Data System (ADS)

    Li, Daijin; Qin, Kan; Luo, Kai

    2015-09-01

    Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.

  6. Solvable Models of Correlated Particles

    NASA Astrophysics Data System (ADS)

    Ha, Zachary Nyong-Chol

    The Heisenberg spin chain with inverse-square exchange (ISE) has recently been introduced and has elevated general interest in the models with ISE. It has been known for a long time that the model is directly related to the random matrix theory. Recently, the matrix model in two -dimensional quantum gravity has also been shown to be related to the ISE model. In this thesis we show that the Bethe -ansatz-solvable, nearest-neighbor-exchange (NNE) models and the ISE model share a striking structure called the "string". Chapter 1 is a review of the Bethe ansatz, the "strings", and the ISE models. In Chapter 2 the "string" structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to show the validity of thermodynamic Bethe ansatz equations (TBAE). We, furthermore, solve TBAE in a strong coupling expansion series form and obtain the thermodynamic potential which agrees with the known high temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some new features of the strongly correlated one -dimensional Hubbard model. In Chapter 3 a one-dimensional quantum N-body system of either fermions or bosons with SU(n) "spins" (or colors in particle physics language) interacting via inverse-square exchange is presented. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product wave function. The class of states we construct corresponds to the ground state and the low-energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state, we find the harmonic fluid parameters (i.e., the charge, spin velocities, etc.) explicitly. The correlation exponent and the compressibility are also found. As expected, the general harmonic relation (i.e., v_ {S} = (v_{N}v_{J })^{1/2) is satisfied among the charge and the spin velocities. In Chapter 4, an

  7. Semi-Empirical Modeling of Two-Dimensional and Three-Dimensional Dynamic Stall

    NASA Astrophysics Data System (ADS)

    Modarres, Ramin

    Helicopters are generally limited in their performance by the phenomenon of dynamic stall. The purpose of this work is to develop a method for modeling dynamic stall that is appropriate to preliminary design and flight simulator applications. Unlike other semi-empirical dynamic stall models, the model developed in this thesis, not only counts for the well-known, three-dimensional flow effects on the stalled loads but also captures the secondary vortex-shedding phenomenon that has been seen in experiments. The fundamental physics that modify dynamic-stall behavior and that have been extended from two-dimensional to three-dimensional flow are, namely: 1.) yawed flow, 2.) time-varying velocity, 3.) the rotational environment and 4.) the radial blade coupling. For the reduced-order modeling, extra nonlinear states have been added to the dynamic stall model in order to simulate the double-dynamic-stall phenomenon. The results of this study will have practical applications to aerospace systems, such as compliant or morphing surfaces in rotary-wing systems that encounter transient or periodic separation and reattachment during phenomena such as dynamic stall.

  8. ICE/ISEE plasma wave data analysis

    NASA Technical Reports Server (NTRS)

    Greenstadt, E. W.

    1992-01-01

    The interval reported on, from Jan. 1990 to Dec. 1991, has been one of continued processing and archiving of ICE plasma wave (pw) data and transition from analysis of ISEE 3 and ICE cometary data to ICE data taken along its cruise trajectory, where coronal mass ejections are the focus of attention. We have continued to examine with great interest the last year of ISEE 3's precomet phase, when it spent considerable time far downwind from Earth, recording conditions upstream, downstream, and across the very weak, distant flank bow shock. Among other motivations was the apparent similarity of some shock and post shock structures to the signatures of the bow wave surrounding comet Giacobini-Zinner, whose ICE-phase data was revisited. While pursuing detailed, second-order scientific inquiries still pending from the late ISEE 3 recordings, we have also sought to position ourselves for study of CME's by instituting a data processing format new to the ISEE 3/ICE pw detector. Processed detector output has always been summarized and archived in 24-hour segments, with all pw channels individually plotted and stacked one above the next down in frequency, with each channel calibrated separately to keep all data patterns equally visible in the plots, regardless of gross differences in energy content at the various frequencies. Since CME's, with their preceding and following solar wind plasmas, can take more than one day to pass by the spacecraft, a more condensed synoptic view of the pw data is required to identify, let alone assess, CME characteristics than has been afforded by the traditional routines. This requirement is addressed in a major new processing initiative in the past two years. Besides our own ongoing and fresh investigations, we have cooperated, within our resources, with studies conducted extramurally by distant colleagues irrespective of the phase of the ISEE 3/ICE mission under scrutiny. The remainder of this report summarizes our processing activities, our

  9. Simulation of upper troposphere CO2 from two-dimensional and three-dimensional models

    NASA Astrophysics Data System (ADS)

    Jiang, X.; Shia, R.; Li, Q.; Chahine, M. T.; Olsen, E. T.; Chen, L. L.; Yung, Y. L.

    2006-12-01

    The Caltech/JPL two-dimensional (2-D) chemistry and transport model (CTM) and three-dimensional (3-D) GEOS-CHEM model have been used to simulate the CO2 in the upper troposphere from 2000 to 2004. Model results agree well with the aircraft observations between 9 km and 13 km [Matsueda et al., Tellus 2002] in the tropics. However, in the mid-latitudes there are some discrepancies between the 3-D GEOS-CHEM simulation and 2-D CTM simulation. The 2-D CTM matches the observations better. The comparison of the profiles between the two model simulations reveals that the exchange between the stratosphere and troposphere in the 3-D model may be too strong in the winter and spring. Specific humidity from GEOS-4 model and AIRS is used as a diagnostic of convection in the 3-D GEOS-CHEM model. While the GEOS-4 specific humidity matches that of AIRS fairly well in the tropics, the agreement is poor at mid-latitudes, where the model does not show enough deep convection. Finally, CO2 simulated by 2-D and 3-D models are compared to the CO2 retrieval from Chahine et al. [GRL 2005].

  10. Fermions in five-dimensional brane world models

    NASA Astrophysics Data System (ADS)

    Smolyakov, Mikhail N.

    2016-06-01

    In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.

  11. On numerical modeling of one-dimensional geothermal histories

    USGS Publications Warehouse

    Haugerud, R.A.

    1989-01-01

    Numerical models of one-dimensional geothermal histories are one way of understanding the relations between tectonics and transient thermal structure in the crust. Such models can be powerful tools for interpreting geochronologic and thermobarometric data. A flexible program to calculate these models on a microcomputer is available and examples of its use are presented. Potential problems with this approach include the simplifying assumptions that are made, limitations of the numerical techniques, and the neglect of convective heat transfer. ?? 1989.

  12. Three-dimensional models. [For orbital celestial mechanics

    SciTech Connect

    Hunter, C. )

    1990-06-01

    The Schwarzschild (1979) approach to the analysis of three-dimensional galactic models is reviewed. An analysis of triaxial Staeckel models is discussed which shows that such models have a wide variety of possible distribution functions. The uniqueness that Schwarzschild first encountered in his discrete formulation of the problem of finding a three-integral distribution function for a triaxial density is real and not an artifact of the finite cell approximation. 27 refs.

  13. Neutral sheet crossings by ISEE-3 in the distant magnetotail

    NASA Technical Reports Server (NTRS)

    Heikkila, W. J.; Slavin, J. A.; Smith, E. J.; Baker, D. N.; Zwickl, R. D.

    1986-01-01

    The magnetic field data from ISEE-3 in the distant magnetotail at crossings of the field reversal (or neutral sheet) region are analyzed to determine the instantaneous direction of the normal component B(z) at the crossing. Crossings in the middle of the aberrated magnetotail near the apogee A2 of the first deep-tail orbit of ISEE-3 in January-February, 1983 were selected. Data for an interval of one hour is discussed at length to illustrate some of the difficulties that can occur. One particular smooth crossing at 15:56 UT, February 4, 1983, shows that complicated microstructure can occur in times shorter than one minute; averaging over long times may eliminate essential information for this purpose. By inspecting the magnetic field data at the highest resolution, however, it is shown that the direction of the plasma sheet flows and the sense of B(z) across the neutral sheet do not always agree with the reconnection models. Rather, they indicate that the low latitude boundary layer may play a significant role in the dynamics of the magnetotail.

  14. Programmers manual for a one-dimensional Lagrangian transport model

    USGS Publications Warehouse

    Schoellhamer, D.H.; Jobson, H.E.

    1986-01-01

    A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program codes. The Programmers Manual is intended for the model user who needs to modify code either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)

  15. Long-range string orders and topological quantum phase transitions in the one-dimensional quantum compass model.

    PubMed

    Wang, Hai Tao; Cho, Sam Young

    2015-01-14

    In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy and fidelity per lattice site by using the infinite matrix product state representation with the infinite time evolving block decimation method. In the whole range of the interaction parameters, we find that four distinct string orders characterize the four different Haldane phases and the topological quantum phase transition occurs between the Haldane phases. The critical exponents of the string order parameters β = 1/8 and the cental charges c = 1/2 at the critical points show that the topological phase transitions between the phases belong to an Ising type of universality classes. In addition to the string order parameters, the singularities of the second derivative of the ground state energies per site, the continuous and singular behaviors of the Von Neumann entropy and the pinch points of the fidelity per lattice site manifest that the phase transitions between the phases are of the second-order, in contrast to the first-order transition suggested in previous studies.

  16. Predicting bite force in mammals: two-dimensional versus three-dimensional lever models.

    PubMed

    Davis, J L; Santana, S E; Dumont, E R; Grosse, I R

    2010-06-01

    Bite force is a measure of whole-organism performance that is often used to investigate the relationships between performance, morphology and fitness. When in vivo measurements of bite force are unavailable, researchers often turn to lever models to predict bite forces. This study demonstrates that bite force predictions based on two-dimensional (2-D) lever models can be improved by including three-dimensional (3-D) geometry and realistic physiological cross-sectional areas derived from dissections. Widely used, the 2-D method does a reasonable job of predicting bite force. However, it does so by over predicting physiological cross-sectional areas for the masseter and pterygoid muscles and under predicting physiological cross-sectional areas for the temporalis muscle. We found that lever models that include the three dimensional structure of the skull and mandible and physiological cross-sectional areas calculated from dissected muscles provide the best predictions of bite force. Models that accurately represent the biting mechanics strengthen our understanding of which variables are functionally relevant and how they are relevant to feeding performance. PMID:20472771

  17. Likelihood-Free Inference in High-Dimensional Models.

    PubMed

    Kousathanas, Athanasios; Leuenberger, Christoph; Helfer, Jonas; Quinodoz, Mathieu; Foll, Matthieu; Wegmann, Daniel

    2016-06-01

    Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza. PMID:27052569

  18. Emergent friction in two-dimensional Frenkel-Kontorova models.

    PubMed

    Norell, Jesper; Fasolino, Annalisa; de Wijn, Astrid S

    2016-08-01

    Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity. PMID:27627382

  19. Likelihood-Free Inference in High-Dimensional Models.

    PubMed

    Kousathanas, Athanasios; Leuenberger, Christoph; Helfer, Jonas; Quinodoz, Mathieu; Foll, Matthieu; Wegmann, Daniel

    2016-06-01

    Methods that bypass analytical evaluations of the likelihood function have become an indispensable tool for statistical inference in many fields of science. These so-called likelihood-free methods rely on accepting and rejecting simulations based on summary statistics, which limits them to low-dimensional models for which the value of the likelihood is large enough to result in manageable acceptance rates. To get around these issues, we introduce a novel, likelihood-free Markov chain Monte Carlo (MCMC) method combining two key innovations: updating only one parameter per iteration and accepting or rejecting this update based on subsets of statistics approximately sufficient for this parameter. This increases acceptance rates dramatically, rendering this approach suitable even for models of very high dimensionality. We further derive that for linear models, a one-dimensional combination of statistics per parameter is sufficient and can be found empirically with simulations. Finally, we demonstrate that our method readily scales to models of very high dimensionality, using toy models as well as by jointly inferring the effective population size, the distribution of fitness effects (DFE) of segregating mutations, and selection coefficients for each locus from data of a recent experiment on the evolution of drug resistance in influenza.

  20. Emergent friction in two-dimensional Frenkel-Kontorova models

    NASA Astrophysics Data System (ADS)

    Norell, Jesper; Fasolino, Annalisa; de Wijn, Astrid S.

    2016-08-01

    Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.

  1. Effects of global brightening on primary production and hypoxia in Ise Bay, Japan

    NASA Astrophysics Data System (ADS)

    Tanaka, Yoji; Kanno, Ariyo; Shinohara, Ryuichiro

    2014-07-01

    In many parts of the world, annual mean surface solar radiation (SSR) has undergone significant decadal changes; however, its effect on the coastal water environment has not been investigated. This study investigates the effects of changes in the SSR on hypoxia and the primary production of phytoplankton in a eutrophic bay in Japan (Ise Bay), where the annual SSR increased by 13.3% from 1980 to 2010. We numerically simulated the hydrodynamics and ecosystem of 2010 using a three-dimensional model (case O). We used this model to simulate the case where SSR was reduced by 10% (case A) and estimated the effect of an increase in SSR from the difference between case O and case A. With the 10% increase in SSR, the primary production in the bay increased by only 2.8%. This limited increase was the result of the negative effects by the nonlinearity of the light limitation function (including the photoinhibition) and the limitation in PO4-P availability and a significant positive effect by the increased water temperature. Similarly, the overall volume of hypoxic water increased, and in August, it increased by 5.8%. This is because water temperature and biomass such as phytoplankton increased with the increase in SSR; consequently, all oxygen consumption terms such as biological respiration also increased. These results imply that recent global brightening has the potential to amplify the primary production and hypoxia in a eutrophic bay.

  2. Local properties of the two-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Drewes, Jan; Miller, Luke; Cocchi, Eugenio; Chan, Chun Fai; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

    2016-05-01

    Quantum gases of interacting fermionic atoms in optical lattices promise to shed new light on the low-temperature phases of the Hubbard model such as spin-ordered phases, or in particular, on possible d-wave superconductivity. In this context it remains challenging to further reduce the temperature of the trapped gas. We experimentally realize the two-dimensional Hubbard model by loading a quantum degenerate Fermi gas of 40K atoms into a three-dimensional optical lattice geometry. By tuning the interaction between the two lowest hyperfine states to strong repulsion the two-dimensional Mott-insulator is created. High resolution absorption imaging in combination with radio-frequency spectroscopy is applied to spatially resolve the atomic distribution in a single layer in the vertical direction. This measurement scheme gives direct access to the local properties of the trapped gas and we present most recent data on the distribution of entropy and density-density fluctuations.

  3. Non-self-averaging in Ising spin glasses and hyperuniversality.

    PubMed

    Lundow, P H; Campbell, I A

    2016-01-01

    Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter U_{22}(T,L) for the spin glass susceptibility [and for higher moments U_{nn}(T,L)] is reported for dimensions 2,3,4,5, and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length ξ(T,L) as U_{nn}(β,L)=[K_{d}ξ(T,L)/L]^{d} and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.3700]. Empirically, it is found that the K_{d} values are independent of d to within the statistics. The maximum values [U_{nn}(T,L)]_{max} are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [U_{nn}(T,L)]_{max} peak values are also practically dimension-independent to within the statistics and so are "hyperuniversal." These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario. PMID:26871035

  4. Non-self-averaging in Ising spin glasses and hyperuniversality

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

    Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter U22(T ,L ) for the spin glass susceptibility [and for higher moments Un n(T ,L ) ] is reported for dimensions 2 ,3 ,4 ,5 , and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length ξ (T ,L ) as Un n(β ,L ) =[Kdξ (T ,L ) /L ] d and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996), 10.1103/PhysRevLett.77.3700]. Empirically, it is found that the Kd values are independent of d to within the statistics. The maximum values [Unn(T,L ) ] max are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [Unn(T,L ) ] max peak values are also practically dimension-independent to within the statistics and so are "hyperuniversal." These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and X Y spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.

  5. Three dimensional modelling of ICRF launchers for fusion devices

    NASA Astrophysics Data System (ADS)

    Carter, M. D.; Rasmussen, D. A.; Ryan, P. M.; Hanson, G. R.; Stallings, D. C.; Batchelor, D. B.; Bigelow, T. S.; England, A. C.; Hoffman, D. J.; Murakami, M.; Wang, C. Y.; Wilgen, J. B.; Rogers, J. H.; Wilson, J. R.; Majeski, R.; Schilling, G.

    1996-02-01

    The three dimensional (3-D) nature of antennas for fusion applications in the ion cyclotron range of frequencies (ICRF) requires accurate modelling to design and analyse new antennas. In this article, analysis and design tools for radiofrequency (RF) antennas are successfully benchmarked with experiment, and the 3-D physics of the launched waves is explored. The systematic analysis combines measured density profiles from a reflectometer system, transmission line circuit modelling, detailed 3-D magnetostatics modelling and a new 3-D electromagnetic antenna model including plasma. This analysis gives very good agreement with measured loading data from the Tokamak Fusion Test Reactor (TFTR) Bay-M antenna, thus demonstrating the validity of the analysis for the design of new RF antennas. The 3-D modelling is contrasted with 2-D models, and significant deficiencies are found in the latter. The 2-D models are in error by as much as a factor of 2 in real and reactive loading, even after they are corrected for the most obvious 3-D effects. Three dimensional effects play the most significant role at low parallel wavenumbers, where the launched power spectrum can be quite different from the predictions of 2-D models. Three dimensional effects should not be ignored for many RF designs, especially those intended for fast wave current drive

  6. Interactive Multimedia and Concrete Three-Dimensional Modelling.

    ERIC Educational Resources Information Center

    Baxter, J. H.; Preece, Peter F. W.

    1999-01-01

    Compares a multimedia package for teaching about the phases of the moon to grade 8 (12-year-old) students with a conventional three-dimensional modeling approach. Results show both methods were equally effective in terms of student learning, for male and female students, and prior computer experience was not a factor in multimedia use. (Author/LRW)

  7. THREE-DIMENSIONAL NAPL FATE AND TRANSPORT MODEL

    EPA Science Inventory

    We have added several new and significant capabilities to UTCHEM to make it into a general-purpose NAPL simulator. The simulator is now capable of modeling transient and steady-state three-dimensional flow and mass transport in the groundwater (saturated) and vadose (unsaturated...

  8. Judgment Research and the Dimensional Model of Personality

    ERIC Educational Resources Information Center

    Garb, Howard N.

    2008-01-01

    Comments on the original article "Plate tectonics in the classification of personality disorder: Shifting to a dimensional model," by T. A. Widiger and T. J. Trull. The purpose of this comment is to address (a) whether psychologists know how personality traits are currently assessed by clinicians and (b) the reliability and validity of those…

  9. A Framework for Dimensionality Assessment for Multidimensional Item Response Models

    ERIC Educational Resources Information Center

    Svetina, Dubravka; Levy, Roy

    2014-01-01

    A framework is introduced for considering dimensionality assessment procedures for multidimensional item response models. The framework characterizes procedures in terms of their confirmatory or exploratory approach, parametric or nonparametric assumptions, and applicability to dichotomous, polytomous, and missing data. Popular and emerging…

  10. A two-dimensional analytical model of petroleum vapor intrusion

    NASA Astrophysics Data System (ADS)

    Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.

    2016-02-01

    In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.

  11. Three dimensional global modeling of atmospheric CO2

    NASA Technical Reports Server (NTRS)

    Fung, I.; Hansen, J.; Rind, D.

    1983-01-01

    A model was developed to study the prospects of extracting information on carbon dioxide sources and sinks from observed CO2 variations. The approach uses a three dimensional global transport model, based on winds from a 3-D general circulation model (GCM), to advect CO2 noninteractively, i.e., as a tracer, with specified sources and sinks of CO2 at the surface. The 3-D model employed is identified and biosphere, ocean and fossil fuel sources and sinks are discussed. Some preliminary model results are presented.

  12. Dynamic Ising model: reconstruction of evolutionary trees

    NASA Astrophysics Data System (ADS)

    de Oliveira, P. M. C.

    2013-09-01

    An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. ‘Species’ here is a general denomination for biological species, spoken languages or any other entity which evolves through heredity. From the N currently alive species within a clade, distances are measured through pairwise comparisons made by geneticists, linguists, etc. The larger is such a distance that, for a pair of species, the older is their last common ancestor. The aim is to reconstruct the previously unknown bifurcations, i.e. the whole clade, from knowledge of the N(N - 1)/2 quoted distances, which are taken for granted. A mechanical method is presented and its applicability is discussed.

  13. Two dimensional modelling of three core cable transient temperature rise

    SciTech Connect

    Lyall, J. )

    1990-01-01

    This paper describes a study of the transient temperature rise of a three core table. Results from a computer program that models the two dimensional heat flow are compared with those obtained using the normally applied one dimensional model. The modelling technique is an alternative to the finite difference and finite element methods. It develops the concept of a thermal resistance/capacitance analogue as can be done using the finite difference method but does so more directly without the need to use the partial differential equation. In addition, it provides the flexibility of the finite element method when modelling a complex geometry and material combination such as that found in a 3-core cable without the complexity of its mathematics.

  14. 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.

  15. 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.

  16. Modeling complexly magnetized two-dimensional bodies of arbitrary shape

    SciTech Connect

    Mariano, J.; Hinze, W.J. . Dept. of Earth and Atmospheric Sciences)

    1993-05-01

    A method has been devised for the forward computation of magnetic anomalies due to two-dimensional (2-D) polygonal bodies with heterogeneously directed magnetization. The calculations are based on the equivalent line source approach wherein the source is subdivided into discrete elements that vary spatially in their magnetic properties. This equivalent dipole line method provides a fast and convenient means of representing and computing magnetic anomalies for bodies possessing complexly varying magnitude and direction of magnetization. The algorithm has been tested and applied to several generalized cases to verify the accuracy of the computation. The technique has also been used to model observed aeromagnetic anomalies associated with the structurally deformed, remanently magnetized Keweenawan volcanic rocks in eastern Lake Superior. This method is also easily adapted to the calculation of anomalies due to two and one-half-dimensional (2.5-D) and three-dimensional (3-D) heterogeneously magnetized sources.

  17. Characterization of the Dilute Ising Antiferromagnet

    SciTech Connect

    Wiener, T.

    2000-09-12

    A spin glass is a magnetic ground state in which ferromagnetic and antiferromagnetic exchange interactions compete, thereby creating frustration and a multidegenerate state with no long range order. An Ising system is a system where the spins are constrained to lie parallel or antiparallel to a primary axis. There has been much theoretical interest in the past ten years in the effects of applying a magnetic field transverse to the primary axis in an Ising spin glass at low temperatures and thus study phase transitions at the T=0 limit. The focus of this study is to search for and characterize a new Ising spin glass system. This is accomplished by site diluting yttrium for terbium in the crystalline material TbNi{sub 2}Ge{sub 2}. The first part of this work gives a brief overview of the physics of rare earth magnetism and an overview of experimental characteristics of spin glasses. This is followed by the methodology used to manufacture the large single crystals used in this study, as well as the measurement techniques used. Next, a summary of the results of magnetic measurements on across the dilution series from pure terbium to pure yttrium is presented. This is followed by detailed measurements on particular dilutions which demonstrate spin glass behavior. Pure TbNi{sub 2}Ge{sub 2} is an Ising antiferromagnet with a several distinct metamagnetic states below 17 K. As the terbium is alloyed with yttrium, these magnetic states are weakened in a consistent manner, as is seen in measurements of the transition temperatures and analysis of Curie-Weiss behavior at high temperature. At low concentrations of terbium, below 35%, long range order is no longer present and a spin-glass-like state emerges. This state is studied through various measurements, dc and ac susceptibility, resistivity, and specific heat. This magnetic behavior was then compared to that of other well characterized spin glasses. It is concluded that there is a region of concentration s for which a spin

  18. A refined one-dimensional rotordynamics model with three-dimensional capabilities

    NASA Astrophysics Data System (ADS)

    Carrera, E.; Filippi, M.

    2016-03-01

    This paper evaluates the vibration characteristics of various rotating structures. The present methodology exploits the one-dimensional Carrera Unified Formulation (1D CUF), which enables one to go beyond the kinematic assumptions of classical beam theories. According to the component-wise (CW) approach, Lagrange-like polynomial expansions (LE) are here adopted to develop the refined displacement theories. The LE elements make it possible to model each structural component of the rotor with an arbitrary degree of accuracy using either different displacement theories or localized mesh refinements. Hamilton's Principle is used to derive the governing equations, which are solved by the Finite Element Method. The CUF one-dimensional theory includes all the effects due to rotation, namely the Coriolis term, spin softening and geometrical stiffening. The numerical simulations have been performed considering a thin ring, discs and bladed-deformable shafts. The effects of the number and the position of the blades on the dynamic stability of the rotor have been evaluated. The results have been compared, when possible, with the 2D and 3D solutions that are available in the literature. CUF models appear very practical to investigate the dynamics of complex rotating structures since they provide 2D and quasi-3D results, while preserving the computational effectiveness of one-dimensional solutions.

  19. 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.

  20. Approaches to verification of two-dimensional water quality models

    SciTech Connect

    Butkus, S.R. . Water Quality Dept.)

    1990-11-01

    The verification of a water quality model is the one procedure most needed by decision making evaluating a model predictions, but is often not adequate or done at all. The results of a properly conducted verification provide the decision makers with an estimate of the uncertainty associated with model predictions. Several statistical tests are available for quantifying of the performance of a model. Six methods of verification were evaluated using an application of the BETTER two-dimensional water quality model for Chickamauga reservoir. Model predictions for ten state variables were compared to observed conditions from 1989. Spatial distributions of the verification measures showed the model predictions were generally adequate, except at a few specific locations in the reservoir. The most useful statistics were the mean standard error of the residuals. Quantifiable measures of model performance should be calculated during calibration and verification of future applications of the BETTER model. 25 refs., 5 figs., 7 tabs.

  1. Crystallization in Ising quantum magnets and Rydberg superatoms

    NASA Astrophysics Data System (ADS)

    Schauss, Peter

    2016-05-01

    Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. In this talk, I will report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Recent results connect these findings with the picture of Rydberg superatoms. We investigated their scalability and observed collective Rabi oscillations with the perspective of using Rydberg superatoms as collective qubits. Experiments performed at Max-Planck Institute of Quantum Optics, Garching, Germany.

  2. Two-dimensional Core-collapse Supernova Models with Multi-dimensional Transport

    NASA Astrophysics Data System (ADS)

    Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun

    2015-02-01

    We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant {O}(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate {O}(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying "ray-by-ray" approach employed by all other groups may be compromising their results. We show that "ray-by-ray" calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion.

  3. TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA MODELS WITH MULTI-DIMENSIONAL TRANSPORT

    SciTech Connect

    Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun E-mail: burrows@astro.princeton.edu

    2015-02-10

    We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant O(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate O(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ''ray-by-ray'' approach employed by all other groups may be compromising their results. We show that ''ray-by-ray'' calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion.

  4. SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL.

    USGS Publications Warehouse

    Hromadka, T.V.; Lai, Chintu

    1985-01-01

    A simplification of the two-dimensional (2-D) continuity and momentum equations is the diffusion equation. To investigate its capability, the numerical model using the diffusion approach is applied to a hypothetical failure problem of a regional water reservoir. The model is based on an explicit, integrated finite-difference scheme, and the floodplain is simulated by a popular home computer which supports 64K FORTRAN. Though simple, the 2-D model can simulate some interesting flooding effects that a 1-D full dynamic model cannot.

  5. Three-dimensional "Mercedes-Benz" model for water.

    PubMed

    Dias, Cristiano L; Ala-Nissila, Tapio; Grant, Martin; Karttunen, Mikko

    2009-08-01

    In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduces the main peaks of the experimental radial distribution function of water. In addition to these structural properties, the model also captures the thermodynamical anomalies of water: The anomalous density profile, the negative thermal expansivity, the large heat capacity, and the minimum in the isothermal compressibility.

  6. Three-dimensional ``Mercedes-Benz'' model for water

    NASA Astrophysics Data System (ADS)

    Dias, Cristiano L.; Ala-Nissila, Tapio; Grant, Martin; Karttunen, Mikko

    2009-08-01

    In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduces the main peaks of the experimental radial distribution function of water. In addition to these structural properties, the model also captures the thermodynamical anomalies of water: The anomalous density profile, the negative thermal expansivity, the large heat capacity, and the minimum in the isothermal compressibility.

  7. Path Integral Solubility of Two-Dimensional Models

    SciTech Connect

    Das, Ashok K.; Mathur, Vishnu S.

    1985-07-01

    We apply the technique of Fujikawa to solve for simple two-dimensional models by looking at the nontrivial transformation properties of the fermion measure in the path-integral formalism. We obtain the most general solution for the massless Thirring model and point out how the one-parameter solution reduces to that of Johnson and Sommerfield in a particular limit. We present the most general solution for the massive vector model indicating how it reduces to the solutions of Brown and Sommerfield for different values of the parameter. The solution of a gradient-coupling model is also discussed.

  8. Three-dimensional "Mercedes-Benz" model for water.

    PubMed

    Dias, Cristiano L; Ala-Nissila, Tapio; Grant, Martin; Karttunen, Mikko

    2009-08-01

    In this paper we introduce a three-dimensional version of the Mercedes-Benz model to describe water molecules. In this model van der Waals interactions and hydrogen bonds are given explicitly through a Lennard-Jones potential and a Gaussian orientation-dependent terms, respectively. At low temperature the model freezes forming Ice-I and it reproduces the main peaks of the experimental radial distribution function of water. In addition to these structural properties, the model also captures the thermodynamical anomalies of water: The anomalous density profile, the negative thermal expansivity, the large heat capacity, and the minimum in the isothermal compressibility. PMID:19673572

  9. Equation of State of the Two-Dimensional Hubbard Model.

    PubMed

    Cocchi, Eugenio; Miller, Luke A; Drewes, Jan H; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

    2016-04-29

    The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0≲U/t≲20 and temperatures, down to k_{B}T/t=0.63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

  10. Equation of State of the Two-Dimensional Hubbard Model.

    PubMed

    Cocchi, Eugenio; Miller, Luke A; Drewes, Jan H; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

    2016-04-29

    The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0≲U/t≲20 and temperatures, down to k_{B}T/t=0.63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches. PMID:27176527

  11. Equation of State of the Two-Dimensional Hubbard Model

    NASA Astrophysics Data System (ADS)

    Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

    2016-04-01

    The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

  12. Three Dimensional Thermal Abuse Reaction Model for Lithium Ion Batteries

    2006-06-29

    Three dimensional computer models for simulating thermal runaway of lithium ion battery was developed. The three-dimensional model captures the shapes and dimensions of cell components and the spatial distributions of materials and temperatures, so we could consider the geometrical features, which are critical especially in large cells. An array of possible exothermic reactions, such as solid-electrolyte-interface (SEI) layer decomposition, negative active/electrolyte reaction, and positive active/electrolyte reaction, were considered and formulated to fit experimental data frommore » accelerating rate calorimetry and differential scanning calorimetry. User subroutine code was written to implement NREL developed approach and to utilize a commercially available solver. The model is proposed to use for simulation a variety of lithium-ion battery safety events including thermal heating and short circuit.« less

  13. 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

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

    SciTech Connect

    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. 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.

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

    PubMed

    Wu, Bin; Iwashita, Takuya; Egami, Takeshi

    2015-11-01

    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. In this paper, 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. The connection between SRPDFs and stress correlation function is explained through an approximation in which the shear stress is replaced by a pseudospin. We further assess the possibility of interpreting the long-range stress correlation as a consequence of short-range Ising-like pseudospin interactions. PMID:26651691

  16. A three-dimensional model of Tangential YORP

    SciTech Connect

    Golubov, O.; Scheeres, D. J.; Krugly, Yu. N.

    2014-10-10

    Tangential YORP, or TYORP, has recently been demonstrated to be an important factor in the evolution of an asteroid's rotation state. It is complementary to normal YORP, or NYORP, which used to be considered previously. While NYORP is produced by non-symmetry in the large-scale geometry of an asteroid, TYORP is due to heat conductivity in stones on the surface of the asteroid. To date, TYORP has been studied only in a simplified one-dimensional model, substituting stones with high long walls. This article for the first time considers TYORP in a realistic three-dimensional model, also including shadowing and self-illumination effects via ray tracing. TYORP is simulated for spherical stones lying on regolith. The model includes only five free parameters and the dependence of the TYORP on each of them is studied. The TYORP torque appears to be smaller than previous estimates from the one-dimensional model, but is still comparable to the NYORP torques. These results can be used to estimate TYORP of different asteroids and also as a basis for more sophisticated models of TYORP.

  17. Statistical mechanics of shell models for two-dimensional turbulence

    NASA Astrophysics Data System (ADS)

    Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

    1994-12-01

    We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

  18. A three-dimensional spin-diffusion model for micromagnetics

    NASA Astrophysics Data System (ADS)

    Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter

    2015-10-01

    We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.

  19. A three-dimensional spin-diffusion model for micromagnetics

    PubMed Central

    Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter

    2015-01-01

    We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796

  20. Two dimensional hydrodynamic modeling of a high latitude braided river

    NASA Astrophysics Data System (ADS)

    Humphries, E.; Pavelsky, T.; Bates, P. D.

    2014-12-01

    Rivers are a fundamental resource to physical, ecologic and human systems, yet quantification of river flow in high-latitude environments remains limited due to the prevalence of complex morphologies, remote locations and sparse in situ monitoring equipment. Advances in hydrodynamic modeling and remote sensing technology allow us to address questions such as: How well can two-dimensional models simulate a flood wave in a highly 3-dimensional braided river environment, and how does the structure of such a flood wave differ from flow down a similar-sized single-channel river? Here, we use the raster-based hydrodynamic model LISFLOOD-FP to simulate flood waves, discharge, water surface height, and velocity measurements over a ~70 km reach of the Tanana River in Alaska. In order to use LISFLOOD-FP a digital elevation model (DEM) fused with detailed bathymetric data is required. During summer 2013, we surveyed 220,000 bathymetric points along the study reach using an echo sounder system connected to a high-precision GPS unit. The measurements are interpolated to a smooth bathymetric surface, using Topo to Raster interpolation, and combined with an existing five meter DEM (Alaska IfSAR) to create a seamless river terrain model. Flood waves are simulated using varying complexities in model solvers, then compared to gauge records and water logger data to assess major sources of model uncertainty. Velocity and flow direction maps are also assessed and quantified for detailed analysis of braided channel flow. The most accurate model output occurs with using the full two-dimensional model structure, and major inaccuracies appear to be related to DEM quality and roughness values. Future work will intercompare model outputs with extensive ground measurements and new data from AirSWOT, an airborne analog for the Surface Water and Ocean Topography (SWOT) mission, which aims to provide high-resolution measurements of terrestrial and ocean water surface elevations globally.

  1. ICE/ISEE plasma wave data analysis

    NASA Technical Reports Server (NTRS)

    Greenstadt, E. W.; Moses, S. L.

    1993-01-01

    This report is one of the final processing of ICE plasma wave (pw) data and analysis of late ISEE 3, ICE cometary, and ICE cruise trajectory data, where coronal mass ejections (CME's) were the first locus of attention. Interest in CME's inspired an effort to represent our pw data in a condensed spectrogram format that facilitated rapid digestion of interplanetary phenomena on long (greater than 1 day) time scales. The format serendipitously allowed us to also examine earth-orbiting data from a new perspective, invigorating older areas of investigation in Earth's immediate environment. We, therefore, continued to examine with great interest the last year of ISEE 3's precomet phase, when it spent considerable time far downwind from Earth, recording for days on end conditions upstream, downstream, and across the very weak, distant flank bow shock. Among other motivations has been the apparent similarity of some shock and post shock structures to the signatures of the bow wave surrounding comet Giacobini-Zinner, whose ICE-phase data we revisited.

  2. Fermion masses and mixing in general warped extra dimensional models

    NASA Astrophysics Data System (ADS)

    Frank, Mariana; Hamzaoui, Cherif; Pourtolami, Nima; Toharia, Manuel

    2015-06-01

    We analyze fermion masses and mixing in a general warped extra dimensional model, where all the Standard Model (SM) fields, including the Higgs, are allowed to propagate in the bulk. In this context, a slightly broken flavor symmetry imposed universally on all fermion fields, without distinction, can generate the full flavor structure of the SM, including quarks, charged leptons and neutrinos. For quarks and charged leptons, the exponential sensitivity of their wave functions to small flavor breaking effects yield hierarchical masses and mixing as it is usual in warped models with fermions in the bulk. In the neutrino sector, the exponential wave-function factors can be flavor blind and thus insensitive to the small flavor symmetry breaking effects, directly linking their masses and mixing angles to the flavor symmetric structure of the five-dimensional neutrino Yukawa couplings. The Higgs must be localized in the bulk and the model is more successful in generalized warped scenarios where the metric background solution is different than five-dimensional anti-de Sitter (AdS5 ). We study these features in two simple frameworks, flavor complimentarity and flavor democracy, which provide specific predictions and correlations between quarks and leptons, testable as more precise data in the neutrino sector becomes available.

  3. Spatial clustering method based on three-dimensional cloud model

    NASA Astrophysics Data System (ADS)

    Wang, Haijun; Wang, Li; Deng, Yu; Liu, Jia

    2008-12-01

    Spatial clustering is one of those major methods applying to spatial data mining and knowledge discovery. The purpose of this paper is to set forth Spatial Clustering Method Based on Multidimensional Cloud Model, which can be widely applied to the research on classification and hierarchy in realm of spatial data mining and knowledge discovery. This paper summarizes all kinds of cloud model and analyzes the optimalizing form of spatial data-three-dimensional cloud model. The limitation which sets the weighing value subjectively in traditional way and propagation of error can be avoided. The implementation procedure of this method is advanced, and the feasibility of this method is proven through experiments effectively.

  4. New data assimilation system DNDAS for high-dimensional models

    NASA Astrophysics Data System (ADS)

    Qun-bo, Huang; Xiao-qun, Cao; Meng-bin, Zhu; Wei-min, Zhang; Bai-nian, Liu

    2016-05-01

    The tangent linear (TL) models and adjoint (AD) models have brought great difficulties for the development of variational data assimilation system. It might be impossible to develop them perfectly without great efforts, either by hand, or by automatic differentiation tools. In order to break these limitations, a new data assimilation system, dual-number data assimilation system (DNDAS), is designed based on the dual-number automatic differentiation principles. We investigate the performance of DNDAS with two different optimization schemes and subsequently give a discussion on whether DNDAS is appropriate for high-dimensional forecast models. The new data assimilation system can avoid the complicated reverse integration of the adjoint model, and it only needs the forward integration in the dual-number space to obtain the cost function and its gradient vector concurrently. To verify the correctness and effectiveness of DNDAS, we implemented DNDAS on a simple ordinary differential model and the Lorenz-63 model with different optimization methods. We then concentrate on the adaptability of DNDAS to the Lorenz-96 model with high-dimensional state variables. The results indicate that whether the system is simple or nonlinear, DNDAS can accurately reconstruct the initial condition for the forecast model and has a strong anti-noise characteristic. Given adequate computing resource, the quasi-Newton optimization method performs better than the conjugate gradient method in DNDAS. Project supported by the National Natural Science Foundation of China (Grant Nos. 41475094 and 41375113).

  5. A THREE-DIMENSIONAL BABCOCK-LEIGHTON SOLAR DYNAMO MODEL

    SciTech Connect

    Miesch, Mark S.; Dikpati, Mausumi

    2014-04-10

    We present a three-dimensional (3D) kinematic solar dynamo model in which poloidal field is generated by the emergence and dispersal of tilted sunspot pairs (more generally bipolar magnetic regions, or BMRs). The axisymmetric component of this model functions similarly to previous 2.5 dimensional (2.5D, axisymmetric) Babcock-Leighton (BL) dynamo models that employ a double-ring prescription for poloidal field generation but we generalize this prescription into a 3D flux emergence algorithm that places BMRs on the surface in response to the dynamo-generated toroidal field. In this way, the model can be regarded as a unification of BL dynamo models (2.5D in radius/latitude) and surface flux transport models (2.5D in latitude/longitude) into a more self-consistent framework that builds on the successes of each while capturing the full 3D structure of the evolving magnetic field. The model reproduces some basic features of the solar cycle including an 11 yr periodicity, equatorward migration of toroidal flux in the deep convection zone, and poleward propagation of poloidal flux at the surface. The poleward-propagating surface flux originates as trailing flux in BMRs, migrates poleward in multiple non-axisymmetric streams (made axisymmetric by differential rotation and turbulent diffusion), and eventually reverses the polar field, thus sustaining the dynamo. In this Letter we briefly describe the model, initial results, and future plans.

  6. Ising superconductivity and Majorana fermions in transition-metal dichalcogenides

    NASA Astrophysics Data System (ADS)

    Zhou, Benjamin T.; Yuan, Noah F. Q.; Jiang, Hong-Liang; Law, K. T.

    2016-05-01

    In monolayer transition-metal dichalcogenides (TMDs), electrons in opposite K valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originating from in-plane mirror symmetry breaking, pins the electron spins to the out-of-plane directions, and results in Ising superconducting states with strongly enhanced upper critical fields. Here, we show that the Ising SOC generates equal-spin-triplet Cooper pairs with spin polarized in the in-plane directions. Importantly, the spin-triplet Cooper pairs can induce superconducting pairings in a half-metal wire placed on top of the TMD and result in a topological superconductor with Majorana end states. Direct ways to detect equal-spin triplet Cooper pairs and the differences between Ising superconductors and Rashba superconductors are discussed.

  7. Neutral sheet crossings by ISEE-3 in the distant magnetotail

    NASA Technical Reports Server (NTRS)

    Heikkila, W. J.; Slavin, J. A.; Smith, E. J.; Baker, D. N.; Zwickl, R. D.

    1986-01-01

    Magnetic field data from ISEE-3 in the distant magnetotail at crossings of the field reversal (or neutral sheet) region were analyzed to determine the instantaneous direction of the normal component Bz at the crossing. A crossing identified as being almost always tailward of the steady-state X-line was selected. Data for 1 hr are discussed to illustrate difficulties. One particular smooth crossing shows that complicated microstructure can occur in times less than 1 min. Averaging over long times may eliminate essential information. Inspection of the magnetic field data at the highest resolution, however, shows that the direction of the plasma sheet flows and the sense of Bz across the neutral sheet do not always agree with the reconnection models. Rather, they indicate that the low latitude boundary layer may play a significant role in the dynamics of the magnetotail.

  8. Destroying a topological quantum bit by condensing Ising vortices.

    PubMed

    Hao, Zhihao; Inglis, Stephen; Melko, Roger

    2014-12-09

    The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm.

  9. Quantum annealing speedup over simulated annealing on random Ising chains

    NASA Astrophysics Data System (ADS)

    Zanca, Tommaso; Santoro, Giuseppe E.

    2016-06-01

    We show clear evidence of a quadratic speedup of a quantum annealing (QA) Schrödinger dynamics over a Glauber master equation simulated annealing (SA) for a random Ising model in one dimension, via an equal-footing exact deterministic dynamics of the Jordan-Wigner fermionized problems. This is remarkable, in view of the arguments of H. G. Katzgraber et al. [Phys. Rev. X 4, 021008 (2014), 10.1103/PhysRevX.4.021008], since SA does not encounter any phase transition, while QA does. We also find a second remarkable result: that a "quantum-inspired" imaginary-time Schrödinger QA provides a further exponential speedup, i.e., an asymptotic residual error decreasing as a power law τ-μ of the annealing time τ .

  10. Three-dimensional radiation transfer modeling in a dicotyledon leaf

    NASA Astrophysics Data System (ADS)

    Govaerts, Yves M.; Jacquemoud, Stéphane; Verstraete, Michel M.; Ustin, Susan L.

    1996-11-01

    The propagation of light in a typical dicotyledon leaf is investigated with a new Monte Carlo ray-tracing model. The three-dimensional internal cellular structure of the various leaf tissues, including the epidermis, the palisade parenchyma, and the spongy mesophyll, is explicitly described. Cells of different tissues are assigned appropriate morphologies and contain realistic amounts of water and chlorophyll. Each cell constituent is characterized by an index of refraction and an absorption coefficient. The objective of this study is to investigate how the internal three-dimensional structure of the tissues and the optical properties of cell constituents control the reflectance and transmittance of the leaf. Model results compare favorably with laboratory observations. The influence of the roughness of the epidermis on the reflection and absorption of light is investigated, and simulation results confirm that convex cells in the epidermis focus light on the palisade parenchyma and increase the absorption of radiation.

  11. Modeling and Experimentation on a Two-dimensional Synthetic jet

    NASA Astrophysics Data System (ADS)

    Wang, Yunfei; Mohseni, Kamran

    2007-11-01

    Hotwire anemometry is employed in order to investigate the spatial development of a two-dimensional synthetic jet. Flow velocity at various locations downstream from a slit is measured. A self similar behavior in the measured velocity is observed. An analytical model for a steady synthetic jet is developed that accurately matches the experimental data. As observed by other groups, the two-dimensional synthetic jet spreads at a rate higher than a continuous jet. This rate is accurately predicted by our model. It is identified that the main difference between a continuous jet and a synthetic jet is the higher value of the virtual viscosity (eddy viscosity) in a synthetic jet. This is attributed to the pulsate nature of a synthetic jet that makes it more susceptible to turbulence.

  12. Phase Diagram of Symmetric Two-Dimensional Traffic Model

    NASA Astrophysics Data System (ADS)

    Ishibashi, Yoshihiro; Fukui, Minoru

    2016-10-01

    On the basis of the critical car density line in the phase diagram of the Biham-Middleton-Levine model for symmetric two-dimensional traffic systems, the formula of the flow in the intermediate jam flow phase is hypothesized. The formula is utilized to obtain the phase boundary between the free flow and jam flow phases, where the flow becomes maximum. The validity of this phase boundary has been confirmed by simulations.

  13. An algebraic turbulence model for three-dimensional viscous flows

    NASA Technical Reports Server (NTRS)

    Chima, R. V.; Giel, P. W.; Boyle, R. J.

    1993-01-01

    An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

  14. Tipping Points in 1-Dimensional Schelling Models with Switching Agents

    NASA Astrophysics Data System (ADS)

    Barmpalias, George; Elwes, Richard; Lewis-Pye, Andy

    2015-02-01

    Schelling's spacial proximity model was an early agent-based model, illustrating how ethnic segregation can emerge, unwanted, from the actions of citizens acting according to individual local preferences. Here a 1-dimensional unperturbed variant is studied under switching agent dynamics, interpretable as being open in that agents may enter and exit the model. Following the authors' work (Barmpalias et al., FOCS, 2014) and that of Brandt et al. (Proceedings of the 44th ACM Symposium on Theory of Computing (STOC 2012), 2012), rigorous asymptotic results are established. The dynamic allows either type to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a generalization of the models considered in [1] and [3], the model's parameters comprise the initial proportions of the two types, along with independent values of the tolerance for each type. This model comprises a 1-dimensional spin-1 model with spin dependent external field, as well as providing an example of cascading behaviour within a network.

  15. On multiscale approaches to three-dimensional modelling of morphogenesis

    PubMed Central

    Chaturvedi, R; Huang, C; Kazmierczak, B; Schneider, T; Izaguirre, J.A; Glimm, T; Hentschel, H.G.E; Glazier, J.A; Newman, S.A; Alber, M.S

    2005-01-01

    In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction–diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb. PMID:16849182

  16. Three-dimensional numerical model for soil vapor extraction.

    PubMed

    Nguyen, Van Thinh; Zhao, Lian; Zytner, Richard G

    2013-04-01

    Mass transfer limitations impact the effectiveness of soil vapor extraction (SVE) and cause tailing. In order to identify the governing mass transfer processes, a three-dimensional SVE numerical model was developed. The developed model was based on Comsol Multiphysics a finite element method that incorporates multi-phase flow, multi-component transport and non-equilibrium transient mass transfer. Model calibration was done against experimental data from previously completed lab-scale reactor experiments. The developed model, 3D-SVE, nicely simulates laboratory findings and allows for changes in the important governing mass transfer relationships. The modeling results showed that a single averaged mass transfer value is a poor representation of the entire SVE operation, and that a transient mass transfer coefficient is required to fully represent SVE tailing. Calibration of the lab scale model showed that the most important mass transfer occurs between the NAPL and vapor phase.

  17. Three-dimensional thermochemical nonequilibrium flow modeling for hypersonic flows

    NASA Technical Reports Server (NTRS)

    Tam, L. T.; Li, C. P.

    1989-01-01

    A three-dimensional thermochemical nonequilibrium model has been developed and applied to the study of entry flows surrounding space vehicles. The model accounts for both chemical and vibrational nonequilibrium phenomena behind the bow shock. The thermodynamic state of a real gas is modeled with a translational-rotational temperature and a electron-vibrational temperature. Their internal energies are averaged to determine the temperature used in the reaction rates calculation. In order to establish the validity of the selected models, both one- and two-temperature models with seven and/or eleven species were investigated. Several numerical experiments that include a sphere, the RAMC vehicle and 3D AFE forebody flows were performed. Preliminary results were compared with RAMC-II experimental data. Good agreement was obtained after a two-temperature model with eleven species and thirty reactions was incorporated into the study.

  18. Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

    The spin-1/2 Ising-Heisenberg two-leg ladder accounting for alternating Ising and Heisenberg inter-leg couplings in addition to the Ising intra-leg coupling is rigorously mapped onto to a mixed spin-(3/2,1/2) Ising-Heisenberg diamond chain with the nodal Ising spins S = 3 / 2 and the interstitial spin-1/2 Heisenberg dimers. The latter effective model with higher-order interactions between the nodal and interstitial spins is subsequently exactly solved within the transfer-matrix method. The model under investigation exhibits five different ground states: ferromagnetic, antiferromagnetic, superantiferromagnetic and two types of frustrated ground states with a non-zero residual entropy. A detailed study of thermodynamic properties reveals an anomalous specific-heat peak at low enough temperatures, which is strongly reminiscent because of its extraordinary height and sharpness to an anomaly accompanying a phase transition. It is convincingly evidenced, however, that the anomalous peak in the specific heat is finite and it comes from vigorous thermal excitations from a two-fold degenerate ground state towards a macroscopically degenerate excited state. Thermal entanglement between the nearest-neighbor Heisenberg spins is also comprehensively explored by taking advantage of the concurrence. The threshold temperature delimiting a boundary between the entangled and disentangled parameter space may show presence of a peculiar temperature reentrance.

  19. Signatures from an extra-dimensional seesaw model

    SciTech Connect

    Blennow, Mattias; Melbeus, Henrik; Ohlsson, Tommy; Zhang He

    2010-08-15

    We study the generation of small neutrino masses in an extra-dimensional model, where singlet fermions are allowed to propagate in the extra dimension, while the standard model particles are confined to a brane. Motivated by the fact that extra-dimensional models are nonrenormalizable, we truncate the Kaluza-Klein towers at a maximal Kaluza-Klein number. This truncation, together with the structure of the bulk Majorana mass term, motivated by the Sherk-Schwarz mechanism, implies that the Kaluza-Klein modes of the singlet fermions pair to form Dirac fermions, except for a number of unpaired Majorana fermions at the top of each tower. These heavy Majorana fermions are the only sources of lepton number breaking in the model, and similarly to the type-I seesaw mechanism, they naturally generate small masses for the left-handed neutrinos. The lower Kaluza-Klein modes mix with the light neutrinos, and the mixing effects are not suppressed with respect to the light-neutrino masses. Compared to conventional fermionic seesaw models, such mixing can be more significant. We study the signals of this model at the Large Hadron Collider, and find that the current low-energy bounds on the nonunitarity of the leptonic mixing matrix are strong enough to exclude an observation.

  20. Three-dimensional Model of Tissue and Heavy Ions Effects

    NASA Technical Reports Server (NTRS)

    Ponomarev, Artem L.; Sundaresan, Alamelu; Huff, Janice L.; Cucinotta, Francis A.

    2007-01-01

    A three-dimensional tissue model was incorporated into a new Monte Carlo algorithm that simulates passage of heavy ions in a tissue box . The tissue box was given as a realistic model of tissue based on confocal microscopy images. The action of heavy ions on the cellular matrix for 2- or 3-dimensional cases was simulated. Cells were modeled as a cell culture monolayer in one example, where the data were taken directly from microscopy (2-d cell matrix), and as a multi-layer obtained from confocal microscopy (3-d case). Image segmentation was used to identify cells with precise areas/volumes in an irradiated cell culture monolayer, and slices of tissue with many cell layers. The cells were then inserted into the model box of the simulated physical space pixel by pixel. In the case of modeled tissues (3-d), the tissue box had periodic boundary conditions imposed, which extrapolates the technique to macroscopic volumes of tissue. For the real tissue (3-d), specific spatial patterns for cell apoptosis and necrosis are expected. The cell patterns were modeled based on action cross sections for apoptosis and necrosis estimated from current experimental data. A spatial correlation function indicating a higher spatial concentration of damaged cells from heavy ions relative to the low-LET radiation cell damage pattern is presented. The spatial correlation effects among necrotic cells can help studying microlesions in organs, and probable effects of directionality of heavy ion radiation on epithelium and endothelium.

  1. A Multi-Dimensional Classification Model for Scientific Workflow Characteristics

    SciTech Connect

    Ramakrishnan, Lavanya; Plale, Beth

    2010-04-05

    Workflows have been used to model repeatable tasks or operations in manufacturing, business process, and software. In recent years, workflows are increasingly used for orchestration of science discovery tasks that use distributed resources and web services environments through resource models such as grid and cloud computing. Workflows have disparate re uirements and constraints that affects how they might be managed in distributed environments. In this paper, we present a multi-dimensional classification model illustrated by workflow examples obtained through a survey of scientists from different domains including bioinformatics and biomedical, weather and ocean modeling, astronomy detailing their data and computational requirements. The survey results and classification model contribute to the high level understandingof scientific workflows.

  2. Three Dimensional Modeling of an MRI Actuated Steerable Catheter System.

    PubMed

    Liu, Taoming; Cavuşoğlu, M Cenk

    2014-01-01

    This paper presents the three dimensional kinematic modeling of a novel steerable robotic ablation catheter system. The catheter, embedded with a set of current-carrying micro-coils, is actuated by the magnetic forces generated by the magnetic field of the MRI scanner. This paper develops a 3D model of the MRI actuated steerable catheter system by using finite differences approach. For each finite segment, a quasi-static torque-deflection equilibrium equation is calculated using beam theory. By using the deflection displacements and torsion angles, the kinematic modeling of the catheter system is derived. The proposed models are evaluated by comparing the simulation results of the proposed model with the experimental results of a proof-of-concept prototype. PMID:25328804

  3. Two-Dimensional Quantum Model of a Nanotransistor

    NASA Technical Reports Server (NTRS)

    Govindan, T. R.; Biegel, B.; Svizhenko, A.; Anantram, M. P.

    2009-01-01

    A mathematical model, and software to implement the model, have been devised to enable numerical simulation of the transport of electric charge in, and the resulting electrical performance characteristics of, a nanotransistor [in particular, a metal oxide/semiconductor field-effect transistor (MOSFET) having a channel length of the order of tens of nanometers] in which the overall device geometry, including the doping profiles and the injection of charge from the source, gate, and drain contacts, are approximated as being two-dimensional. The model and software constitute a computational framework for quantitatively exploring such device-physics issues as those of source-drain and gate leakage currents, drain-induced barrier lowering, and threshold voltage shift due to quantization. The model and software can also be used as means of studying the accuracy of quantum corrections to other semiclassical models.

  4. The NASA Ames Research Center one- and two-dimensional stratospheric models. Part 2: The two-dimensional model

    NASA Technical Reports Server (NTRS)

    Whitten, R. C.; Borucki, W. J.; Watson, V. R.; Shimazaki, T.; Woodward, H. T.; Riegel, C. A.; Capone, L. A.; Becker, T.

    1977-01-01

    The two-dimensional model of stratospheric constituents is presented in detail. The derivation of pertinent transport parameters and the numerical solution of the species continuity equations, including a technique for treating the stiff differential equations that represent the chemical kinetic terms, and appropriate methods for simulating the diurnal variations of the solar zenith angle and species concentrations are discussed. Predicted distributions of tracer constituents (ozone, carbon 14, nitric acid) are compared with observed distributions.

  5. Three-dimensional face model reproduction method using multiview images

    NASA Astrophysics Data System (ADS)

    Nagashima, Yoshio; Agawa, Hiroshi; Kishino, Fumio

    1991-11-01

    This paper describes a method of reproducing three-dimensional face models using multi-view images for a virtual space teleconferencing system that achieves a realistic visual presence for teleconferencing. The goal of this research, as an integral component of a virtual space teleconferencing system, is to generate a three-dimensional face model from facial images, synthesize images of the model virtually viewed from different angles, and with natural shadow to suit the lighting conditions of the virtual space. The proposed method is as follows: first, front and side view images of the human face are taken by TV cameras. The 3D data of facial feature points are obtained from front- and side-views by an image processing technique based on the color, shape, and correlation of face components. Using these 3D data, the prepared base face models, representing typical Japanese male and female faces, are modified to approximate the input facial image. The personal face model, representing the individual character, is then reproduced. Next, an oblique view image is taken by TV camera. The feature points of the oblique view image are extracted using the same image processing technique. A more precise personal model is reproduced by fitting the boundary of the personal face model to the boundary of the oblique view image. The modified boundary of the personal face model is determined by using face direction, namely rotation angle, which is detected based on the extracted feature points. After the 3D model is established, the new images are synthesized by mapping facial texture onto the model.

  6. Spacecraft potential control on ISEE-1

    NASA Technical Reports Server (NTRS)

    Gonfalone, A.; Pedersen, A.; Fahleson, U. V.; Faelthammar, C. G.; Mozer, F. S.; Torbert, R. B.

    1979-01-01

    Active control of the potential of the ISEE-1 satellite by the use of electron guns is reviewed. The electron guns contain a special cathode capable of emitting an electron current selectable between 10 to the -8th power and 10 to the -3rd power at energies from approximately .6 to 41 eV. Results obtained during flight show that the satellite potential can be stabilized at a value more positive than the normally positive floating potential. The electron guns also reduce the spin modulation of the spacecraft potential which is due to the aspect dependent photoemission of the long booms. Plasma parameters like electron temperature and density can be deduced from the variation of the spacecraft potential as a function of the gun current. The effects of electron beam emission on other experiments are briefly mentioned.

  7. Transient Loschmidt echo in quenched Ising chains

    NASA Astrophysics Data System (ADS)

    Lupo, Carla; Schiró, Marco

    2016-07-01

    We study the response to sudden local perturbations of highly excited quantum Ising spin chains. The key quantity encoding this response is the overlap between time-dependent wave functions, which we write as a transient Loschmidt Echo. Its asymptotics at long time differences contain crucial information about the structure of the highly excited nonequilibrium environment induced by the quench. We compute the echo perturbatively for a weak local quench but for arbitrarily large global quench, using a cumulant expansion. Our perturbative results suggest that the echo decays exponentially, rather than power law as in the low-energy orthogonality catastrophe, a further example of quench-induced decoherence already found in the case of quenched Luttinger liquids. The emerging decoherence scale is set by the strength of the local potential and the bulk excitation energy.

  8. Hypergeometric Forms for Ising-Class Integrals

    SciTech Connect

    Bailey, David H.; Borwein, David; Borwein, Jonathan M.; Crandall,Richard E.

    2006-07-01

    We apply experimental-mathematical principles to analyzecertain integrals relevant to the Ising theory of solid-state physics. Wefind representations of the these integrals in terms of MeijerG-functions and nested-Barnes integrals. Our investigations began bycomputing 500-digit numerical values of Cn,k,namely a 2-D array of Isingintegrals for all integers n, k where n is in [2,12]and k is in [0,25].We found that some Cn,k enjoy exact evaluations involving DirichletL-functions or the Riemann zeta function. In theprocess of analyzinghypergeometric representations, we found -- experimentally and strikingly-- that the Cn,k almost certainly satisfy certain inter-indicialrelations including discrete k-recursions. Using generating functions,differential theory, complex analysis, and Wilf-Zeilberger algorithms weare able to prove some central cases of these relations.

  9. Goldilocks models of higher-dimensional inflation (including modulus stabilization)

    NASA Astrophysics Data System (ADS)

    Burgess, C. P.; Enns, Jared J. H.; Hayman, Peter; Patil, Subodh P.

    2016-08-01

    We explore the mechanics of inflation within simplified extra-dimensional models involving an inflaton interacting with the Einstein-Maxwell system in two extra dimensions. The models are Goldilocks-like inasmuch as they are just complicated enough to include a mechanism to stabilize the extra-dimensional size (or modulus), yet simple enough to solve explicitly the full extra-dimensional field equations using only simple tools. The solutions are not restricted to the effective 4D regime with H ll mKK (the latter referring to the characteristic mass splitting of the Kaluza-Klein excitations) because the full extra-dimensional Einstein equations are solved. This allows an exploration of inflationary physics in a controlled calculational regime away from the usual four-dimensional lamp-post. The inclusion of modulus stabilization is important because experience with string models teaches that this is usually what makes models fail: stabilization energies easily dominate the shallow potentials required by slow roll and so open up directions to evolve that are steeper than those of the putative inflationary direction. We explore (numerically and analytically) three representative kinds of inflationary scenarios within this simple setup. In one the radion is trapped in an inflaton-dependent local minimum whose non-zero energy drives inflation. Inflation ends as this energy relaxes to zero when the inflaton finds its own minimum. The other two involve power-law scaling solutions during inflation. One of these is a dynamical attractor whose features are relatively insensitive to initial conditions but whose slow-roll parameters cannot be arbitrarily small; the other is not an attractor but can roll much more slowly, until eventually transitioning to the attractor. The scaling solutions can satisfy H > mKK, but when they do standard 4D fluctuation calculations need not apply. When in a 4D regime the solutions predict η simeq 0 and so r simeq 0.11 when ns simeq 0.96 and so

  10. One-dimensional Hubbard-Luttinger model for carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Ishkhanyan, H. A.; Krainov, V. P.

    2015-06-01

    A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low temperatures. The low-lying excitations in one-dimensional electron gas are described in terms of interacting bosons. The Bogolyubov transformation allows one to describe the system as an ensemble of non-interacting quasi-bosons. Operators of Fermi excitations and Green functions of fermions are introduced. The electric current is derived as a function of potential difference on the contact between a nanotube and a normal metal. Deviations from Ohm law produced by electron-electron short-range repulsion as well as by the transverse quantization in single-wall nanotubes are discussed. The results are compared with experimental data.

  11. Upstream waves simultaneously observed by ISEE and UKS

    NASA Technical Reports Server (NTRS)

    Russell, C. T.; Luhmann, J. G.; Elphic, R. C.; Southwood, D. J.; Smith, M. F.

    1987-01-01

    Measurements obtained in the solar wind by ISEE-2 and the United Kingdom Subsatellite (UKS) have been examined for observations of upstream waves. These data reveal that the waves in the foreshock region are enhanced at all frequencies from at least 0.003 Hz to 0.5 Hz. The wave spectra generally have a spectral peak, but this peak is usually broad and the peak frequency depends on the position of the spacecraft. Generally, the spectra seen at the two spacecraft are most similar at high frequencies and least similar at low frequencies. The geometry of the interaction is displayed in the plane containing the magnetic field, the solar wind velocity, and the spacecraft location. However, this coordinate system does not order all the observed wave properties. It does not clearly explain or order the handedness of the waves, or their direction of propagation. It is clear that the upstream region is inherently three-dimensional. The position-dependent nature of the upstream waves indicates that comparisons between ground-based measurements and in-situ observations must be undertaken with some caution.

  12. Upstream waves simultaneously observed by ISEE and UKS

    SciTech Connect

    Russell, C.T.; Luhmann, J.G.; Elphic, R.C. ); Southwood, D.J. ); Smith, M.F.; Johnstone, A.D. )

    1987-07-01

    Measurements obtained in the solar wind by ISEE-2 and the United Kingdom Subsatellite (UKS) have been examined for observations of upstream waves. These data reveal that the waves in the foreshock region are enhanced at all frequencies from at least 0.003 Hz to 0.5 Hz. The wave spectra generally have a spectral peak, but this peak is usually broad and the peak frequency depends on the position of the spacecraft. Generally, the spectra seen at the two spacecraft are most similar at high frequencies and least similar at low frequencies. The geometry of the interaction is displayed in the plane containing the magnetic field, the solar wind velocity, and the spacecraft location. However, this coordinate system does not order all the observed wave properties. It does not clearly explain or order the handedness of the waves, or their direction of propagation. It is clear that the upstream region is inherently three-dimensional. The position-dependent nature of the upstream waves indicates that comparisons between ground-based measurements and in-situ observations must be undertaken with some caution.

  13. Towards automatic calibration of 2-dimensional flood propagation models

    NASA Astrophysics Data System (ADS)

    Fabio, P.; Aronica, G. T.; Apel, H.

    2009-11-01

    Hydraulic models for flood propagation description are an essential tool in many fields, e.g. civil engineering, flood hazard and risk assessments, evaluation of flood control measures, etc. Nowadays there are many models of different complexity regarding the mathematical foundation and spatial dimensions available, and most of them are comparatively easy to operate due to sophisticated tools for model setup and control. However, the calibration of these models is still underdeveloped in contrast to other models like e.g. hydrological models or models used in ecosystem analysis. This has basically two reasons: first, the lack of relevant data against the models can be calibrated, because flood events are very rarely monitored due to the disturbances inflicted by them and the lack of appropriate measuring equipment in place. Secondly, especially the two-dimensional models are computationally very demanding and therefore the use of available sophisticated automatic calibration procedures is restricted in many cases. This study takes a well documented flood event in August 2002 at the Mulde River in Germany as an example and investigates the most appropriate calibration strategy for a full 2-D hyperbolic finite element model. The model independent optimiser PEST, that gives the possibility of automatic calibrations, is used. The application of the parallel version of the optimiser to the model and calibration data showed that a) it is possible to use automatic calibration in combination of 2-D hydraulic model, and b) equifinality of model parameterisation can also be caused by a too large number of degrees of freedom in the calibration data in contrast to a too simple model setup. In order to improve model calibration and reduce equifinality a method was developed to identify calibration data with likely errors that obstruct model calibration.

  14. A three-dimensional transport model for the middle atmosphere

    NASA Technical Reports Server (NTRS)

    Rasch, Philip J.; Tie, Xuexi; Boville, Byron A.; Williamson, David L.

    1994-01-01

    In this paper we describe fundamental properties of an 'off-line' three-dimensional transport model, that is, a model which uses prescribed rather than predicted winds. The model is currently used primarily for studying problems of the middle atmosphere because we have not (yet) incorporated a formulation for the convective transport of trace species, a prerequisite for many tropospheric problems. The off-line model is simpler and less expensive than a model which predicts the wind and mass evolution (an 'on-line' model), but it is more complex than the two-dimensional (2-D) zonally averaged transport models often used in the study of chemistry and transport in the middle atmosphere. It thus serves as a model of intermediate complexity and can fill a useful niche for the study of transport and chemistry. We compare simulations of four tracers, released in the lower stratosphere, in both the on- and off-line models to document the difference resulting from differences in modeling the same problem with this intermediate model. These differences identify the price to be paid in going to a cheaper and simpler calculation. The off-line model transports a tracer in three dimensions. For this reason, it requires fewer approximations than 2-D transport model, which must parameterize the effects of mixing by transient and zonally asymmetric wind features. We compare simulations of the off-line model with simulations of a 2-D model for two problems. First, we compare 2-D and three-dimensional (3-D) models by simulating the emission of an NO(x)-like tracer by a fleet of high-speed aircraft. The off-line model is then used to simulate the transport of C-14 and to contrast its simulation properties to that of the host of 2-D models which participated in an identical simulation in a recent NASA model intercomparison. The off-line model is shown to be somewhat sensitive to the sampling strategy for off-line winds. Simulations with daily averaged winds are in very good qualitative

  15. Some peculiarities in the behavior of non-Ising spin glasses

    NASA Astrophysics Data System (ADS)

    Tareyeva, E. E.; Schelkacheva, T. I.; Chtchelkatchev, N. M.

    2015-03-01

    This paper is a review. We outline the main directions in the modern theory of spin glasses. The main content is based on our recent papers, devoted to studying replica symmetry breaking in non-Ising spin glasses. Studying a series of generalized models showed a certain uniformity of the behavior of these generalized spin glasses. Essentially, we observe a significant difference between their behavior and the behavior of the known systems with random couplings of Ising spins—the Sherrington-Kirkpatrick model and the corresponding p-spin model. We find the bifurcation point for the solution with the first replica symmetry breaking, study the form and stability of the solution near the bifurcation point, and show in which cases the transition to the glass state occurs continuously and in which cases, with a jump of the order parameters.

  16. Tricritical Ising phase transition in a two-ladder Majorana fermion lattice

    NASA Astrophysics Data System (ADS)

    Zhu, Xiaoyu; Franz, M.

    2016-05-01

    We introduce a two-ladder lattice model with interacting Majorana fermions that could be realized on the surfaces of a topological insulator film. We study this model with a combination of analytical and numerical techniques, and we find a phase diagram that features both gapless and gapped phases as well as interesting phase transitions including a quantum critical point in the tricritical Ising (TCI) universality class. The latter occurs at an intermediate-coupling strength at a meeting point of a first-order transition line and an Ising critical line, and it is known to be described by a superconformal field theory with central charge c =7/10 . We discuss the experimental feasibility of constructing the model and tuning parameters to the vicinity of the TCI point where signatures of the elusive supersymmetry can be observed.

  17. Two-dimensional numerical modeling of the Rheasilvia impact formation

    NASA Astrophysics Data System (ADS)

    Ivanov, B. A.; Melosh, H. J.

    2013-07-01

    We numerically modeled the formation of Rheasilvia crater, an enormous impact basin centered on asteroid 4 Vesta's south pole. Using a trial and error method, our models were adjusted to produce the best possible fit to Rheasilvia's size and shape, as observed during the Vesta orbital stage of the Dawn mission. The final model yields estimates of the shock wave decay, escaped material volume, depth of excavation, and other relevant characteristics, to the extent allowed by the two-dimensional (axially symmetric) approximation of the Simplified Arbitrary Lagrangian Eulerian hydrocode. Our model results permit interpretation of the Dawn data on Vesta's shape, topographic crater profiles, and the origin of the Vestoid asteroid family as escaped ejecta from the Rheasilvia crater.

  18. TRANSMISSION SPECTRA OF THREE-DIMENSIONAL HOT JUPITER MODEL ATMOSPHERES

    SciTech Connect

    Fortney, J. J.; Shabram, M.; Showman, A. P.; Lian, Y.; Lewis, N. K.; Freedman, R. S.; Marley, M. S.

    2010-02-01

    We compute models of the transmission spectra of planets HD 209458b, HD 189733b, and generic hot Jupiters. We examine the effects of temperature, surface gravity, and metallicity for the generic planets as a guide to understanding transmission spectra in general. We find that carbon dioxide absorption at 4.4 and 15 mum is prominent at high metallicity, and is a clear metallicity indicator. For HD 209458b and HD 189733b, we compute spectra for both one-dimensional and three-dimensional model atmospheres and examine the differences between them. The differences are usually small, but can be large if atmospheric temperatures are near important chemical abundance boundaries. The calculations for the three-dimensional atmospheres, and their comparison with data, serve as constraints on these dynamical models that complement the secondary eclipse and light curve data sets. For HD 209458b, even if TiO and VO gases are abundant on the dayside, their abundances can be considerably reduced on the cooler planetary limb. However, given the predicted limb temperatures and TiO abundances, the model's optical opacity is too high. For HD 189733b we find a good match with some infrared data sets and constrain the altitude of a postulated haze layer. For this planet, substantial differences can exist between the transmission spectra of the leading and trailing hemispheres, which are an excellent probe of carbon chemistry. In thermochemical equilibrium, the cooler leading hemisphere is methane-dominated, and the hotter trailing hemisphere is CO-dominated, but these differences may be eliminated by non-equilibrium chemistry due to vertical mixing. It may be possible to constrain the carbon chemistry of this planet, and its spatial variation, with James Webb Space Telescope.

  19. A 2-dimensional model of the Venus ionosphere

    SciTech Connect

    McGary, J.E.

    1988-01-01

    The Pioneer Venus observations show a peak in the O{sub 2}{sup +} concentration at {approx}170 km altitude in the dayside ionosphere of Venus. In this thesis, the 2-dimensional MHD equations are solved in a self-consistent manner, as an extension to the 1-dimensional model by Cloutier et al. (1987), to present a global model of the Venus dayside ionosphere for solar zenith angles (SZA) {le} 60{degree}. The model describes, by calculating vertical profiles at different SZA, ion densities, magnetic field magnitudes, and ion velocities. The model shows that the O{sub 2}{sup +} peak, at {approx}170 km altitude, occurs throughout the dayside ionosphere as observed by the Orbiter Ion Mass Spectrometer (OIMS). The velocity field, which affects the ion distributions, is mainly tangential near the ionopause and radial for altitudes below 200 km. The downward flow accelerates, near 170 km altitude, due to collisional interactions with the neutral atmosphere, and removes the O{sub 2}{sup +} densities to lower altitudes, thus, producing the bump observed in the altitude profile.

  20. Three-dimensional Myoblast Aggregates--Effects of Modeled Microgravity

    NASA Technical Reports Server (NTRS)

    Byerly, Diane; Sognier, M. A.; Marquette, M. L.

    2006-01-01

    The overall objective of these studies is to elucidate the molecular and cellular alterations that contribute to muscle atrophy in astronauts caused by exposure to microgravity conditions in space. To accomplish this, a three-dimensional model test system was developed using mouse myoblast cells (C2C12). Myoblast cells were grown as three-dimensional aggregates (without scaffolding or other solid support structures) in both modeled microgravity (Rotary Cell Culture System, Synthecon, Inc.) and at unit gravity in coated Petri dishes. Evaluation of H&E stained thin sections of the aggregates revealed the absence of any necrosis. Confocal microscopy evaluations of cells stained with the Live/Dead assay (Molecular Probes) confirmed that viable cells were present throughout the aggregates with an average of only three dead cells observed per aggregate. Preliminary results from gene array analysis (Affymetrix chip U74Av2) showed that approximately 14% of the genes were down regulated (decreased more than 3 fold) and 4% were upregulated in cells exposed to modeled microgravity for 12 hours compared to unit gravity controls. Additional studies using fluorescent phallacidin revealed a decrease in F-actin in the cells exposed to modeled microgravity compared to unit gravity. Myoblast cells grown as aggregates in modeled microgravity exhibited spontaneous differentiation into syncitia while no differentiation was seen in the unit gravity controls. These studies show that 1)the model test system developed is suitable for assessing cellular and molecular alterations in myoblasts; 2) gene expression alterations occur rapidly (within 12 hours) following exposure to modeled microgravity; and 3) modeled microgravity conditions stimulated myoblast cell differentiation. Achieving a greater understanding of the molecular alterations leading to muscle atrophy will eventually enable the development of cell-based countermeasures, which may be valuable for treatment of muscle diseases on