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Sample records for dimensional ising model

  1. Bootstrapping the Three Dimensional Supersymmetric Ising Model.

    PubMed

    Bobev, Nikolay; El-Showk, Sheer; Mazáč, Dalimil; Paulos, Miguel F

    2015-07-31

    We implement the conformal bootstrap program for three dimensional conformal field theories with N=2 supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the operator product expansion of a chiral and an antichiral primary, we find a kink at the expected location of the critical three dimensional N=2 Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory, as well as the stress-tensor two-point function. We find that the latter is in an excellent agreement with an exact computation.

  2. 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…

  3. 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…

  4. Two-dimensional disordered Ising model within nonextensive statistics

    NASA Astrophysics Data System (ADS)

    Borodikhin, V. N.

    2017-06-01

    In this work, the two-dimensional disordered Ising model with nonextensive Tsallis statistics has been studied for the first time. The critical temperatures and critical indices have been determined for both disordered and uniform models. A new type of critical behavior has been revealed for the disordered model with nonextensive statistics. It has been shown that, within the nonextensive statistics of the two-dimensional Ising model, the Harris criterion is also valid.

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

    PubMed

    Nakayama, Yu

    2016-04-08

    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.

  6. Boundary Critical Behaviour of Two-Dimensional Layered Ising Models

    NASA Astrophysics Data System (ADS)

    Pelizzola, Alessandro

    Layered models are models in which the coupling constants depend in an arbitrary way on one spatial coordinate, usually the distance from a free surface or boundary. Here the theory of the boundary critical behaviour of two-dimensional layered Ising models, including the Hilhorst-van Leeuwen model and models for aperiodic systems, is reviewed, with a particular attention to exact results for the critical behaviour and the boundary order parameter.

  7. Recurrence relations in one-dimensional Ising models

    NASA Astrophysics Data System (ADS)

    da Conceição, C. M. Silva; Maia, R. N. P.

    2017-09-01

    The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.

  8. Two-dimensional XXZ-Ising model with quartic interactions.

    PubMed

    Valverde, J S

    2012-05-01

    In this work we study a two-dimensional XXZ-Ising spin-1/2 model with quartic interactions. The model is composed of a two-dimensional lattice of edge-sharing unitary cells, where each cell consists of two triangular prisms, converging in a basal plane with four Ising spin-1/2 (open circles); the apical positions are also occupied by four Heisenberg spin-1/2 (solid circles). Interaction of the base plane containing the multispin Ising interaction has the parameter J_{4}, and the other pairwise interactions have parameter J. For the proposed model we construct the phase diagram at zero temperature and give all possible spin configurations. In addition, we investigate two regions where the model can be solved exactly, the free fermion condition (FFC) and the symmetrical eight-vertex condition (SEVC). For this purpose we perform a straightforward mapping for a zero-field eight-vertex model. The necessary conditions for the equivalence are analyzed for all ranges of the interaction parameters. Unfortunately, the present model does not satisfy the FFC unless the trivial case; however, it was possible to give a region where the model can be solved approximately. We study the SEVC and verify that this condition is always satisfied. We also explore and discuss the critical conditions giving the region where these critical points are relevant.

  9. Corner wetting transition in the two-dimensional Ising model

    NASA Astrophysics Data System (ADS)

    Lipowski, Adam

    1998-07-01

    We study the interfacial behavior of the two-dimensional Ising model at the corner of weakened bonds. Monte Carlo simulations results show that the interface is pinned to the corner at a lower temperature than a certain temperature Tcw at which it undergoes a corner wetting transition. The temperature Tcw is substantially lower than the temperature of the ordinary wetting transition with a line of weakened bonds. A solid-on-solid-like model is proposed, which provides a supplementary description of the corner wetting transition.

  10. Complete wetting in the three-dimensional transverse Ising model

    NASA Astrophysics Data System (ADS)

    Harris, A. B.; Micheletti, C.; Yeomans, J. M.

    1996-08-01

    We consider a three-dimensional Ising model in a transverse magnetic field h and a bulk field H. An interface is introduced by an appropriate choice of boundary conditions. At the point ( H=0, h=0) spin configurations corresponding to different positions of the interface are degenerate. By studying the phase diagram near this multiphase point using quantum mechanical perturbation theory, we show that the quantum fluctuations, controlled by h, split the multiphase degeneracy giving rise to an infinite sequence of layering transitions.

  11. Pluralism in the critical phenomena of the one-dimensional continuous-spin Ising model

    NASA Astrophysics Data System (ADS)

    Baker, George A., Jr.

    1988-05-01

    A concrete example is given which shows that the one-dimensional Ising and Gaussian model universality classes do not exhaust the universality classes of the one-dimensional continuous-spin Ising model. Thus the normal universality hypothesis fails in this simple, readily analyzable model.

  12. Pluralism in the critical phenomena of the one-dimensional continuous-spin Ising model

    SciTech Connect

    Baker G.A. Jr.

    1988-05-02

    A concrete example is given which shows that the one-dimensional Ising and Gaussian model universality classes do not exhaust the universality classes of the one-dimensional continuous-spin Ising model. Thus the normal universality hypothesis fails in this simple, readily analyzable model.

  13. Scale invariance implies conformal invariance for the three-dimensional Ising model.

    PubMed

    Delamotte, Bertrand; Tissier, Matthieu; Wschebor, Nicolás

    2016-01-01

    Using the Wilson renormalization group, we show that if no integrated vector operator of scaling dimension -1 exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition is fulfilled in all dimensions for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model.

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

    PubMed

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

    2017-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

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

  16. Overlap distribution of the three-dimensional Ising model.

    PubMed

    Berg, Bernd A; Billoire, Alain; Janke, Wolfhard

    2002-10-01

    We study the Parisi overlap probability density P(L)(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point, P(L)(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multioverlap MC algorithm. Below the critical temperature, interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.

  17. 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.

  18. Monte Carlo Study of One-Dimensional Ising Models with Long-Range Interactions

    NASA Astrophysics Data System (ADS)

    Tomita, Yusuke

    2009-01-01

    Recently, Fukui and Todo have proposed a new effective Monte Carlo algorithm for long-range interacting systems. Using the algorithm with the nonequilibrium relaxation method, we investigated long-range interacting one-dimensional Ising models both ferromagnetic and antiferromagnetic with the nearest-neighbor ferromagnetic interaction. For the antiferromagnetic model, we found the systems are paramagnetic at finite temperatures.

  19. Universality class of the two-dimensional site-diluted Ising model.

    PubMed

    Martins, P H L; Plascak, J A

    2007-07-01

    In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.

  20. Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model.

    PubMed

    Ron, Dorit; Brandt, Achi; Swendsen, Robert H

    2017-05-01

    We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

  1. Star-triangle approach to boundary behavior in the two-dimensional Ising model

    NASA Astrophysics Data System (ADS)

    Burkhardt, Theodore W.; Guim, Ihnsouk

    Hilhorst and van Leeuwen showed how to calculate boundary properties of the Ising model on the triangular lattice by iterating a mapping based on the star-triangle transformation. We apply this approach to the Ising model with homogeneous initial couplings in both the semi-infinite and strip geometries. Several exact results for the boundary correlation length and the magnetization are reproduced. The correlation-dimensionality transition for enhanced edge couplings (dual of Abraham’s interface-unbinding transition) is also considered.

  2. Two-dimensional Ising model with competing interactions: Phase diagram and low-temperature remanent disorder

    NASA Astrophysics Data System (ADS)

    O'Hare, A.; Kusmartsev, F. V.; Kugel, K. I.

    2009-01-01

    The two-dimensional Ising model with competing nearest-neighbor and diagonal interactions on the square lattice is studied by the transfer-matrix technique and by the Monte Carlo simulations. The phase diagram of this model is constructed with a special emphasis to the analysis of a glassy state arising as an order to disorder transition at low temperatures. Evidence of the glassy state (based, in particular, on the calculation of the average length of domain walls and on the Edwards-Anderson order parameter) and its characteristics are presented. It was shown that, in the frustrated Ising model, the domain-wall length correlates to the onset of the glassy state, that is, it may play the role of the order parameter for the Ising glass or for glasslike states in other frustrated magnetic systems.

  3. Modeling of the financial market using the two-dimensional anisotropic Ising model

    NASA Astrophysics Data System (ADS)

    Lima, L. S.

    2017-09-01

    We have used the two-dimensional classical anisotropic Ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market. The model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets. We have obtained the mean price in terms of the strong of the site anisotropy term Δ which reinforces the sensitivity of the agent's sentiment to external news.

  4. Simplified transfer matrix approach in the two-dimensional Ising model with various boundary conditions

    NASA Astrophysics Data System (ADS)

    Kastening, Boris

    2002-11-01

    A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.

  5. 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

    2016-11-01

    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.

  6. Correlations in the two-dimensional random-field Ising model

    SciTech Connect

    Glaus, U.

    1986-09-01

    Using transfer matrices, we calculate the connected and disconnected correlation functions of the random-field Ising model on long strips of width N-italic< or =8. The results, where extrapolated to the thermodynamic limit, are in good qualitative agreement with neutron scattering experiments of Birgeneau e-italict-italic a-italicl-italic. (Phys. Rev. B 28, 1438 (1983)) on the two-dimensional dilute Ising-like antiferromagnet Rb/sub 2/Co/sub 0.7/Mg/sub 0.3/F/sub 4/ . For a particular probability distribution of the random field we propose that this model describes an adsorbed monolayer with a doubly degenerate ground state in the presence of frozen impurities and predict some features that could be detected with low-energy electron diffraction experiments on such systems. A modified mean-field theory gives a good qualitative account of the high-temperature behavior of the correlations of this model.

  7. Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state.

    PubMed

    Környei, László; Pleimling, Michel; Iglói, Ferenc

    2008-01-01

    The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.

  8. Static and dynamic structure factors in three-dimensional randomly diluted Ising models.

    PubMed

    Calabrese, Pasquale; Pelissetto, Andrea; Vicari, Ettore

    2008-02-01

    We consider the three-dimensional randomly diluted Ising model and study the critical behavior of the static and dynamic spin-spin correlation functions (static and dynamic structure factors) at the paramagnetic-ferromagnetic transition in the high-temperature phase. We consider a purely relaxational dynamics without conservation laws, the so-called model A. We present Monte Carlo simulations and perturbative field-theoretical calculations. While the critical behavior of the static structure factor is quite similar to that occurring in pure Ising systems, the dynamic structure factor shows a substantially different critical behavior. In particular, the dynamic correlation function shows a large-time decay rate which is momentum independent. This effect is not related to the presence of the Griffiths tail, which is expected to be irrelevant in the critical limit, but rather to the breaking of translational invariance, which occurs for any sample and which, at the critical point, is not recovered even after the disorder average.

  9. Boundary magnetization of a two-dimensional Ising model with inhomogeneous nearest-neighbor interactions

    NASA Astrophysics Data System (ADS)

    Pelizzola, Alessandro

    1994-11-01

    An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst-van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.

  10. Slicing the three-dimensional Ising model: Critical equilibrium and coarsening dynamics.

    PubMed

    Arenzon, Jeferson J; Cugliandolo, Leticia F; Picco, Marco

    2015-03-01

    We study the evolution of spin clusters on two-dimensional slices of the three-dimensional Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly with time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on two-dimensional slices of the three-dimensional system, compared with the behavior of the bidimensional model.

  11. Two-Dimensional Wang-Landau Sampling of AN Asymmetric Ising Model

    NASA Astrophysics Data System (ADS)

    Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.

    We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang-Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

  12. Kovacs effect in the one-dimensional Ising model: A linear response analysis

    NASA Astrophysics Data System (ADS)

    Ruiz-García, M.; Prados, A.

    2014-01-01

    We analyze the so-called Kovacs effect in the one-dimensional Ising model with Glauber dynamics. We consider small enough temperature jumps, for which a linear response theory has been recently derived. Within this theory, the Kovacs hump is directly related to the monotonic relaxation function of the energy. The analytical results are compared with extensive Monte Carlo simulations, and an excellent agreement is found. Remarkably, the position of the maximum in the Kovacs hump depends on the fact that the true asymptotic behavior of the relaxation function is different from the stretched exponential describing the relevant part of the relaxation at low temperatures.

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

    PubMed

    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.

  14. Eigenstate thermalization in the two-dimensional transverse field Ising model.

    PubMed

    Mondaini, Rubem; Fratus, Keith R; Srednicki, Mark; Rigol, Marcos

    2016-03-01

    We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.

  15. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model

    NASA Astrophysics Data System (ADS)

    Jalabert, Rodolfo A.; Sachdev, Subir

    1991-07-01

    The Ising model on a three-dimensional cubic lattice with all plaquettes in the x-y frustrated plane is studied by use of a Monte Carlo technique; the exchange constants are of equal magnitude, but have varying signs. At zero temperature, the model has a finite entropy and no long-range order. The low-temperature phase is characterized by an order parameter measuring the openZ4 symmetry of lattice rotations which is invariant under Mattis gauge transformation; fluctuations lead to the alignment of frustrated bonds into columns and a fourfold degeneracy. An additional factor-of-2 degeneracy is obtained from a global spin flip. The order vanishes at a critical temperature by a transition that appears to be in the universality class of the D=3, XY model. These results are consistent with the theoretical predictions of Blankschtein et al. This Ising model is related by duality to phenomenological models of two-dimensional frustrated quantum antiferromagnets.

  16. Relaxational processes in the one-dimensional Ising model with long-range interactions

    NASA Astrophysics Data System (ADS)

    Tomita, Yusuke

    2016-12-01

    Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter σ , which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of σ . Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.

  17. Relaxational processes in the one-dimensional Ising model with long-range interactions.

    PubMed

    Tomita, Yusuke

    2016-12-01

    Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter σ, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of σ. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.

  18. Quantum correlation and quantum phase transition in the one-dimensional extended Ising model

    NASA Astrophysics Data System (ADS)

    Zhang, Xi-Zheng; Guo, Jin-Liang

    2017-09-01

    Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.

  19. Criterion for universality-class-independent critical fluctuations: example of the two-dimensional Ising model.

    PubMed

    Clusel, Maxime; Fortin, Jean-Yves; Holdsworth, Peter C W

    2004-10-01

    Order parameter fluctuations for the two-dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T(*) (L) and a locus of magnetic fields B(*) (L) are identified, for which the probability density function is similar to that for the two-dimensional XY model in the spin wave approximation. The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality-class-dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.

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

    PubMed

    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.

  1. Fermions as generalized Ising models

    NASA Astrophysics Data System (ADS)

    Wetterich, C.

    2017-04-01

    We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of products of observables. The map preserves locality properties and can be realized for arbitrary dimensions. We present a simple example where a quantum field theory for free massless Dirac fermions in two-dimensional Minkowski space is represented by an asymmetric Ising model on a euclidean square lattice.

  2. 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.

  3. 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.

  4. Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model

    NASA Astrophysics Data System (ADS)

    Pich, C.; Young, A. P.

    1998-03-01

    We study the quantum phase transition in the random transverse-field Ising model by Monte Carlo simulations. In one-dimension it has been established that this system has the following striking behavior: (i) the dynamical exponent is infinite, and (ii) the exponents for the divergence of the average and typical correlation lengths are different. An important issue is whether this behavior is special to one-dimension or whether similar behavior persists in higher dimensions. Here we attempt to answer this question by studies of the two-dimensional model. Our simulations use the Wolff cluster algorithm and the results are analyzed by anisotropic finite size scaling, paying particular attention to the Binder ratio of moments of the order parameter distribution and the distribution of the spin-spin correlation functions for various distances.

  5. Dynamic Critical Exponents of Three-Dimensional Ising Models and Two-Dimensional Three-States Potts Models

    NASA Astrophysics Data System (ADS)

    Murase, Yohsuke; Ito, Nobuyasu

    2008-01-01

    Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization λm (=β/zν) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.

  6. Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model

    NASA Astrophysics Data System (ADS)

    Wu, X.-T.; Abraham, D. B.; Indekeu, J. O.

    2016-01-01

    The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling Js to bulk coupling J , and becomes of first order in the limit Js/J →∞ . However, for Js/J ≫1 , the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3 /2 .

  7. 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

  8. Apparent First-Order Wetting and Anomalous Scaling in the Two-Dimensional Ising Model.

    PubMed

    Wu, X-T; Abraham, D B; Indekeu, J O

    2016-01-29

    The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling J_{s} to bulk coupling J, and becomes of first order in the limit J_{s}/J→∞. However, for J_{s}/J≫1, the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.

  9. Three-dimensional Ising model of polarity formation in molecular crystals

    NASA Astrophysics Data System (ADS)

    Cannavacciuolo, Luigi; Hulliger, Jürg

    2017-10-01

    Polarity formation in a three-dimensional array of molecules is described as a symmetry breaking effect of a generalized Ising Hamiltonian. Geometrical constraints in conjunction with asymmetric multipole interactions are able to break the spin flip symmetry generating a non-vanishing average local polarization.

  10. Light cone in the two-dimensional transverse-field Ising model in time-dependent mean-field theory

    NASA Astrophysics Data System (ADS)

    Hafner, J.; Blass, B.; Rieger, H.

    2016-12-01

    We investigate the propagation of a local perturbation in the two-dimensional transverse-field Ising model with a time-dependent application of the mean-field theory based on the BBGKY hierarchy. We show that the perturbation propagates through the system with a finite velocity and that there is a transition from Manhattan to Euclidian metric, resulting in a light cone with an almost circular shape at sufficiently large distances. The propagation velocity of the perturbation defining the front of the light cone is discussed with respect to the parameters of the Hamiltonian and compared to exact results for the transverse-field Ising model in one dimension.

  11. Long-range dependence of the two-dimensional Ising model at critical temperature

    NASA Astrophysics Data System (ADS)

    Pipiras, Vladas; Taqqu, Murad S.

    2015-03-01

    The paper gives probabilists who are unfamiliar with the Ising model a coherent, integrated explanation of why the Ising model displays long-range dependence at critical temperature. The Ising model in two dimensions involves spins σj,k = ±1 located at every node (j,k) of the lattice, with nearest neighbor interactions. We shall focus on the covariances [{E}{σ _0},_0{σ _0}{,_N}] and [{E}{σ _0},_0{σ _N}{,_N}] between the spin at the origin and the spin located either on the axis at (0,N) or located on the diagonal at (N,N), when the temperature equals a critical value. Using a recent formulation of the so-called `Szegö's theorem', we explain why these covariances decrease to zero like N-1/4 as N → ∞, thus at a slow enough rate so as to exhibit long-range dependence.

  12. Noise-driven dynamic phase transition in a one-dimensional Ising-like model.

    PubMed

    Sen, Parongama

    2010-03-01

    The dynamical evolution of a recently introduced one-dimensional model [S. Biswas and P. Sen, Phys. Rev. E 80, 027101 (2009)] (henceforth, referred to as model I), has been made stochastic by introducing a parameter beta such that beta=0 corresponds to the Ising model and beta-->infinity to the original model I. The equilibrium behavior for any value of beta is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent z , that for any beta not equal 0 , the system belongs to the dynamical class of model I indicating a dynamic phase transition at beta=0. On the other hand, the persistence probabilities in a system of L spins saturate at a value Psat(beta,L)=(beta/L)alphafbeta, where alpha remains constant for all beta not equal 0 supporting the existence of the dynamic phase transition at beta=0. The scaling function f(beta) shows a crossover behavior with f(beta)=constant for beta1 and f(beta) proportional, variantbeta-alpha for beta1.

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

    PubMed Central

    Blaß, Benjamin; Rieger, Heiko

    2016-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Blaß, Benjamin; Rieger, Heiko

    2016-12-01

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

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

    PubMed

    Blaß, Benjamin; Rieger, Heiko

    2016-12-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-09-01

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

  17. Cluster Monte Carlo: Scaling of systematic errors in the two-dimensional Ising model

    SciTech Connect

    Shchur, L.N.; Bloete, H.W.

    1997-05-01

    We present an extensive analysis of systematic deviations in Wolff cluster simulations of the critical Ising model, using random numbers generated by binary shift registers. We investigate how these deviations depend on the lattice size, the shift-register length, and the number of bits correlated by the production rule. They appear to satisfy scaling relations. {copyright} {ital 1997} {ital The American Physical Society}

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

    NASA Astrophysics Data System (ADS)

    Hobrecht, Hendrik; Hucht, Alfred

    2017-02-01

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

  19. Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

    NASA Astrophysics Data System (ADS)

    Bosia, C.; Caselle, M.; Corá, D.

    2010-02-01

    The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e., the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the two-dimensional Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show both with theoretical arguments and numerical simulations that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modeled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-one-dimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the time scale of the nucleation process even in presence of very small amounts of chemoattractants.

  20. 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.

  1. 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.

  2. 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.

  3. Critical behavior and out-of-equilibrium dynamics of a two-dimensional Ising model with dynamic couplings

    NASA Astrophysics Data System (ADS)

    Pinto, Oscar A.; Romá, Federico; Bustingorry, Sebastian

    2014-12-01

    We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest neighbors of each spin pair, which prevents the system from ordering in a full ferromagnetic or antiferromagnetic state. Using a parallel-tempering Monte Carlo algorithm, we find that the model undergoes a continuous phase transition at finite temperature, which belongs to the Ising universality class. The properties of the bond structure and the ground-state entropy are also studied. Finally, we analyze the out-of-equilibrium dynamics which displays typical glassy characteristics at a temperature well below the critical one.

  4. Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line

    NASA Astrophysics Data System (ADS)

    Papakonstantinou, T.; Malakis, A.

    2013-01-01

    We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (pz=0;pxy=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.

  5. Critical behavior of the three-dimensional Ising model with anisotropic bond randomness at the ferromagnetic-paramagnetic transition line.

    PubMed

    Papakonstantinou, T; Malakis, A

    2013-01-01

    We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  7. Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model.

    PubMed

    Dalmazi, D; Sá, F L

    2010-11-01

    We show here for the one-dimensional spin-1/2 axial-next-to-nearest-neighbor Ising model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent σ=-2/3 at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer-matrix eigenvalues. If this condition is absent we have the usual value σ=-1/2 . Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of σ=-2/3 which might be a one-dimensional footprint of a tricritical version of the Yang-Lee edge singularity possibly present also in higher-dimensional spin models.

  8. Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions

    NASA Astrophysics Data System (ADS)

    Janke, W.; Kenna, R.

    2002-03-01

    The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak and for the pseudocritical points. All corrections to scaling are found to be analytic and the shift exponent λ does not coincide with the inverse of the correlation length exponent 1/ν.

  9. Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions

    NASA Astrophysics Data System (ADS)

    Janke, W.; Kenna, R.

    The two-dimensional Ising model with Brascamp-Kunz boundary conditions has a partition function more amenable to analysis than its counterpart on a torus. This fact is exploited to exactly determine the full finite-size scaling behaviour of the Fisher zeroes of the model. Moreover, exact results are also determined for the scaling of the specific heat at criticality, for the specific-heat peak and for the pseudocritical points. All corrections to scaling are found to be analytic and the shift exponent λ does not coincide with the inverse of the correlation length exponent 1/ν.

  10. Learning planar Ising models

    DOE PAGES

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

    2016-12-01

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

  11. Learning planar Ising models

    SciTech Connect

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

    2016-12-01

    Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the 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. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.

  12. 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.

  13. Interface delocalization in the three-dimensional Ising model with a defect plane

    NASA Astrophysics Data System (ADS)

    Benyoussef, A.; El Kenz, A.

    1993-02-01

    Using mean-field theory, the finite-cluster approximation, and the real-space renormalization group, we study the spin-1/2 Ising model on a cubic lattice with a defect plane that divides the system into two semi-infinite ones. The phase diagrams, which represent the connection between defect-plane order and wetting phenomena, are given in the case of two equivalent semi-infinite systems (the same coupling) and in the case of different semi-infinite systems. These phase diagrams are in agreement with those conjectured qualitatively by Igloi and Indekeu.

  14. 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.

  15. Finite-size scaling relations for a four-dimensional Ising model on Creutz cellular automatons

    NASA Astrophysics Data System (ADS)

    Merdan, Z.; Güzelsoy, E.

    2011-06-01

    The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 ≤ L ≤ 8. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of Tc(∞), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value Tc(∞) = 6.6803(1), the cluster Monte Carlo value Tc(∞) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm Tc(∞) = 6.6802632 ± 5 . 10-5. The average values calculated for the critical exponent of the specific heat are α =- 0.0402(15), - 0.0393(12), - 0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, α =- 0.0391(11), agrees with the series expansions result, α =- 0.12 ± 0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, α ≥ 0 ± 0.04. However, α =- 0.0391(11) is inconsistent with the renormalization group prediction of α = 0.

  16. Studies of hysteresis in two-dimensional kinetic Ising model using the FORC technique

    NASA Astrophysics Data System (ADS)

    Robb, Daniel; Novotny, Mark; Rikvold, Per Arne

    2004-03-01

    We describe the FORC (first order reversal curve) technique [1] for hysteresis, first developed as an experimental method to better characterize magnetic materials, and present FORC distributions for simulations of a square-lattice kinetic Ising model. To understand the simulation results, we apply a theory of magnetization reversal for the multidroplet (MD) regime [2] for homogeneous nucleation and growth, also called the Kolmogorov-Johnson-Mehl-Avrami regime. The FORC `partial hysteresis' loops exhibit different properties than those of systems with strong disorder [1]. We compare the simulation and the theory for several lattice sizes, frequencies of the external field, and temperatures. [1] C.R. Pike, A.P. Roberts, and K.L. Verosub, J. Appl. Phys. 85, 6660 (1999). [2] S.W. Sides, P.A. Rikvold, and M.A. Novotny, Phys. Rev. E 59, 2710 (1999).

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

    PubMed

    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.

  18. Topological Characterization of Extended Quantum Ising Models.

    PubMed

    Zhang, G; Song, Z

    2015-10-23

    We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.

  19. Topological Characterization of Extended Quantum Ising Models

    NASA Astrophysics Data System (ADS)

    Zhang, G.; Song, Z.

    2015-10-01

    We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic X Y model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the X Y model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is shown that the variation of the ground state energy density, which is a function of the loop, experiences a nonanalytical point when the winding number of the corresponding loop changes. The winding number can serve as a topological quantum number of the quantum phases in the extended quantum Ising model, which sheds some light upon the relation between quantum phase transition and the geometrical order parameter characterizing the phase diagram.

  20. Corner wetting in the two-dimensional Ising model: Monte Carlo results

    NASA Astrophysics Data System (ADS)

    Albano, E. V.; DeVirgiliis, A.; Müller, M.; Binder, K.

    2003-01-01

    Square L × L (L = 24-128) Ising lattices with nearest neighbour ferromagnetic exchange are considered using free boundary conditions at which boundary magnetic fields ± h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field -h acts. For temperatures T less than the critical temperature Tc of the bulk, this boundary condition leads to the formation of two domains with opposite orientations of the magnetization direction, separated by an interface which for T larger than the filling transition temperature Tf (h) runs from the upper left corner to the lower right corner, while for T < Tf (h) this interface is localized either close to the lower left corner or close to the upper right corner. Numerous theoretical predictions for the critical behaviour of this 'corner wetting' or 'wedge filling' transition are tested by Monte Carlo simulations. In particular, it is shown that for T = Tf (h) the magnetization profile m(z) in the z-direction normal to the interface is simply linear and the interfacial width scales as w propto L, while for T > Tf (h) it scales as w proptosurd L. The distribution P (ell) of the interface position ell (measured along the z-direction from the corners) decays exponentially for T < Tf (h) from either corner, is essentially flat for T = Tf (h) and is a Gaussian centred at the middle of the diagonal for T > Tf (h). Furthermore, the Monte Carlo data are compatible with langleellrangle propto (Tf (h) - T)-1 and a finite size scaling of the total magnetization according to M(L, T) = tilde M {(1 - T/Tf (h))nubot L} with nubot = 1. Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.

  1. Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach

    NASA Astrophysics Data System (ADS)

    Mazzeo, Giorgio; Kühn, Reimer

    1999-10-01

    The equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two-dimensional Ising model in the presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to putting the equilibrium ensemble approach to work. A method by which to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely, the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open to both possibilities. A critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite-size data.

  2. Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach.

    PubMed

    Mazzeo, G; Kühn, R

    1999-10-01

    The equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two-dimensional Ising model in the presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to putting the equilibrium ensemble approach to work. A method by which to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely, the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open to both possibilities. A critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite-size data.

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

    NASA Astrophysics Data System (ADS)

    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 Tc 1 to embody the total landscape of initial conditions at a second critical temperature Tc 2, with Tc 1≈1.59 and Tc 2≈2.11 in J /kB units. It appears that Tc 2 is close to the Onsager result Tc≈2.27 . The transition, which is first-order-like, exhibits a vertical jump to the disorder phase at Tc 2, 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 Tc≈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.

  4. 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.

  5. 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.

  6. SMJ's analysis of Ising model correlation functions

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.; Kohmoto, Mahito

    1980-05-01

    In a series of recent publications Sato, Miwa, and Jimbo (SMJ) have shown how to derive multispin correlation functions of the two-dimensional Ising model in the continuum, or scaling, limit by analyzing the behavior of the solutions to the two-dimensional version of the Dirac equation. The major purpose of the present work is to describe SMJ's analysis more discursively and in terms closer to that used in previous studies of the Ising model. In addition, new and more compact expressions for their basic equations are derived. A single new answer is obtained: the form of the three-spin correlation function at criticality.

  7. Quasi-additive estimates on the Hamiltonian for the one-dimensional long range Ising model

    NASA Astrophysics Data System (ADS)

    Littin, Jorge; Picco, Pierre

    2017-07-01

    In this work, we study the problem of getting quasi-additive bounds for the Hamiltonian of the long range Ising model, when the two-body interaction term decays proportionally to 1/d2 -α , α ∈(0,1 ) . We revisit the paper by Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] where they extend to the case α ∈[0 ,ln3/ln2 -1 ) the result of the existence of a phase transition by using a Peierls argument given by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)] for α =0 . The main arguments of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)] are based in a quasi-additive decomposition of the Hamiltonian in terms of hierarchical structures called triangles and contours, which are related to the original definition of contours introduced by Fröhlich and Spencer [Commun. Math. Phys. 84, 87-101 (1982)]. In this work, we study the existence of a quasi-additive decomposition of the Hamiltonian in terms of the contours defined in the work of Cassandro et al. [J. Math. Phys. 46, 053305 (2005)]. The most relevant result obtained is Theorem 4.3 where we show that there is a quasi-additive decomposition for the Hamiltonian in terms of contours when α ∈[0,1 ) but not in terms of triangles. The fact that it cannot be a quasi-additive bound in terms of triangles lead to a very interesting maximization problem whose maximizer is related to a discrete Cantor set. As a consequence of the quasi-additive bounds, we prove that we can generalise the [Cassandro et al., J. Math. Phys. 46, 053305 (2005)] result, that is, a Peierls argument, to the whole interval α ∈[0,1 ) . We also state here the result of Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] about cluster expansions which implies that Theorem 2.4 that concerns interfaces and Theorem 2.5 that concerns n point truncated correlation functions in Cassandro et al. [Commun. Math. Phys. 327, 951-991 (2014)] are valid for all α ∈[0,1 ) instead of only α ∈[0 ,ln3/ln2 -1 ) .

  8. Damage spreading at the corner-filling transition in the two-dimensional Ising model

    NASA Astrophysics Data System (ADS)

    Rubio Puzzo, M. Leticia; Albano, Ezequiel V.

    2007-01-01

    The propagation of damage on the square Ising lattice with a corner geometry is studied by means of Monte Carlo simulations. By imposing free boundary conditions at which competing boundary magnetic fields ± h are applied, the system undergoes a filling transition at a temperature Tf(h) lower than the Onsager critical temperature TC. The competing fields cause the formation of two magnetic domains with opposite orientation of the magnetization, separated by an interface that for T larger than Tf(h) (but Tmodel) given by ηWT = 0.91(1). However, for later times the propagation crosses to a new regime such as η** = 0.40(2), which is due to the propagation of the damage into the bulk of the magnetic domains. This result can be understood as being due to the constraints imposed on the propagation of damage by the corner geometry of the system that cause healing at the corners where the interface is attached. The critical points for the damage-spreading transition (TD(h)) are evaluated by extrapolation to the thermodynamic limit by using a finite-size scaling approach. Considering error bars, an overlap between the filling and the damage-spreading transitions is found, such that Tf(h) = TD(h). The probability distribution of the damage average position P(l0D) and that of the interface between magnetic domains of different orientation P(l0) are evaluated

  9. Finite-size scaling in two-dimensional Ising spin-glass models.

    PubMed

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

    2011-11-01

    We study the finite-size behavior of two-dimensional spin-glass models. We consider the ±J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL(1/ν) in the ±J model. We find that it holds asymptotically. This result is consistent with the low-temperature crossover scenario in which the crossover temperature, which separates the universal high-temperature region from the discrete low-temperature regime, scales as T(c)(L)~L(-θ(S)) with θ(S)≈0.5.

  10. Quantum Ising model coupled with conducting electrons

    NASA Astrophysics Data System (ADS)

    Yamashita, Yasufumi; Yonemitsu, Kenji

    2005-01-01

    The effect of photo-doping on the quantum paraelectric SrTiO3 is studied by using the one-dimensional quantum Ising model, where the Ising spin describes the effective lattice polarization of an optical phonon. Two types of electron-phonon couplings are introduced through the modulation of transfer integral via lattice deformations. After the exact diagonalization and the perturbation studies, we find that photo-induced low-density carriers can drastically alter quantum fluctuations when the system locates near the quantum critical point between the quantum para- and ferro-electric phases.

  11. An Exact Closed Formula of a Spin-spin Correlation Function of the Two-Dimensional Ising Model with Finite Size

    NASA Astrophysics Data System (ADS)

    Mei, T.

    2015-10-01

    Some expressions of spin-spin correlation functions of the two-dimensional Ising model in the thermodynamic limit have been obtained, however, so far, no one correlation function that can show long range order of the model with finite size has been obtained. The purpose of this paper is to fill this gap. We present an exact closed formula for the correlation functions of the farthest pairs of spins in a column of the two-dimensional rectangular Ising model with periodic-free boundary condition and finite size by the spinor analysis method. The concrete expression correct to order of magnitude of such correlation functions is presented, from which it is shown clearly how long range order emerges as the decrease of the temperature. Some properties are discussed.

  12. Cluster-algorithm renormalization-group study of universal fluctuations in the two-dimensional Ising model.

    PubMed

    Palma, G; Zambrano, D

    2008-12-01

    In this paper we propose a method to study critical systems numerically, which combines collective-mode algorithms and renormalization group on the lattice. This method is an improved version of the Monte Carlo renormalization group in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature T(L) . "Universal fluctuations" were first proposed in the work of Bramwell, Holdsworth, and Pinton [Nature (London) 396, 552 (1998)] and stated that the probability density function of a global quantity for very dissimilar systems, such as a confined turbulent flow and a two-dimensional (2D) magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution," originally obtained for magnetization in the 2D XY model in the low-temperature region. The results for the critical exponents and the renormalization-group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.

  13. 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.

  14. 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.

  15. Reentrance and ultrametricity in three-dimensional Ising spin glasses

    NASA Astrophysics Data System (ADS)

    Katzgraber, Helmut G.; Thomas, Creighton K.; Hartmann, Alexander K.

    2012-02-01

    We study the three-dimensional Edwards-Anderson Ising spin glass with bimodal disorder with a fraction of 22.8% antiferromagnetic bonds. Parallel tempering Monte Carlo simulations down to very low temperatures show that for this fraction of antiferromagnetic bonds the phase diagram of the system is reentrant, in agreement with previous results. Furthemore, using a clustering analysis, we analyze the ultrametric properties of phase space for this model.

  16. Thermal diode from two-dimensional asymmetrical Ising lattices.

    PubMed

    Wang, Lei; Li, Baowen

    2011-06-01

    Two-dimensional asymmetrical Ising models consisting of two weakly coupled dissimilar segments, coupled to heat baths with different temperatures at the two ends, are studied by Monte Carlo simulations. The heat rectifying effect, namely asymmetric heat conduction, is clearly observed. The underlying mechanisms are the different temperature dependencies of thermal conductivity κ at two dissimilar segments and the match (mismatch) of flipping frequencies of the interface spins.

  17. The ising model on the dynamical triangulated random surface

    SciTech Connect

    Aleinov, I.D.; Migelal, A.A.; Zmushkow, U.V. )

    1990-04-20

    The critical properties of Ising model on the dynamical triangulated random surface embedded in D-dimensional Euclidean space are investigated. The strong coupling expansion method is used. The transition to thermodynamical limit is performed by means of continuous fractions.

  18. Unbinding transition of the interface of a two-dimensional Ising-model system with a defect zone in the bulk

    NASA Astrophysics Data System (ADS)

    Xiong, Guo-Ming

    1991-02-01

    By introducing a defect zone instead of a single defect line in the bulk, a modified form of the AB model of Forgacs, Svrakic, and Privman is investigated. It is found that when the defect zone is far away from the substrate the first-order unbinding transition still exists at a temperature T1 below the critical point of the two-dimensional Ising model, while when it is near the substrate no wetting transition can take place because the inhomogeneity constrains the formation of the wetting layer.

  19. Magnon-bound-state hierarchy for the two-dimensional transverse-field Ising model in the ordered phase

    NASA Astrophysics Data System (ADS)

    Nishiyama, Yoshihiro

    2016-12-01

    In the ordered phase for an Ising ferromagnet, the magnons are attractive to form a series of bound states with the mass gaps, m2 dimensional counterpart, for which the universal hierarchical character remains unclear. We employed the exact diagonalization method, which enables us to calculate the dynamical susceptibility via the continued-fraction expansion. Thereby, we observe a variety of signals including m 2 , 3 , 4, and the spectrum is analyzed with the finite-size-scaling method to estimate the universal mass-gap ratios.

  20. Dominance of Metric Correlations in Two-Dimensional Neuronal Cultures Described through a Random Field Ising Model

    NASA Astrophysics Data System (ADS)

    Hernández-Navarro, Lluís; Orlandi, Javier G.; Cerruti, Benedetta; Vives, Eduard; Soriano, Jordi

    2017-05-01

    We introduce a novel random field Ising model, grounded on experimental observations, to assess the importance of metric correlations in cortical circuits in vitro. Metric correlations arise from both the finite axonal length and the heterogeneity in the spatial arrangement of neurons. The experiments consider the response of neuronal cultures to an external electric stimulation for a gradually weaker connectivity strength between neurons, and in cultures with different spatial configurations. The model can be analytically solved in the metric-free, mean-field scenario. The presence of metric correlations precipitates a strong deviation from the mean field. Null models of the same networks that preserve the distribution of connections recover the mean field. Our results show that metric-inherited correlations in spatial networks dominate the connectivity blueprint, mask the actual distribution of connections, and may emerge as the asset that shapes network dynamics.

  1. Triviality problem and high-temperature expansions of higher susceptibilities for the Ising and scalar-field models in four-, five-, and six-dimensional lattices.

    PubMed

    Butera, P; Pernici, M

    2012-02-01

    High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude ratios that determine the critical equation of state. We have obtained a substantial extension, through order 24, of the high-temperature expansions of the free energy (in presence of a magnetic field) for the Ising models with spin s≥1/2 and for the lattice scalar-field theory with quartic self-interaction on the simple-cubic and the body-centered-cubic lattices in four, five, and six spatial dimensions. A numerical analysis of the higher susceptibilities obtained from these expansions yields results consistent with the widely accepted ideas, based on the renormalization group and the constructive approach to Euclidean quantum field theory, concerning the no-interaction ("triviality") property of the continuum (scaling) limit of spin-s Ising and lattice scalar-field models at and above the upper critical dimensionality.

  2. Magnetic properties and interface delocalization in the three-dimensional Ising model with defect-plane amorphization

    NASA Astrophysics Data System (ADS)

    Benyoussef, A.; El Amraoui, Y.; El Kenz, A.; Kaneyoshi, T.

    1994-02-01

    Magnetic properties and interface delocalization of the spin-1/2 Ising model on a cubic lattice with an amorphized defect plane that divides the system into two semi-infinite ones are investigated by the use of the effective-field theory. The global phase diagrams, which represent the connection between amorphized defect-plane order and wetting transitions (from partial to complete wetting), are given in the case of two equivalent semi-infinite systems (the same coupling) and in the case of different semi-infinite systems. The influence of the amorphization in these global phase diagrams is also studied. Moreover, magnetic properties which illustrate some interesting behavior for the amorphized systems are investigated.

  3. An Ising model for metal-organic frameworks

    NASA Astrophysics Data System (ADS)

    Höft, Nicolas; Horbach, Jürgen; Martín-Mayor, Victor; Seoane, Beatriz

    2017-08-01

    We present a three-dimensional Ising model where lines of equal spins are frozen such that they form an ordered framework structure. The frame spins impose an external field on the rest of the spins (active spins). We demonstrate that this "porous Ising model" can be seen as a minimal model for condensation transitions of gas molecules in metal-organic frameworks. Using Monte Carlo simulation techniques, we compare the phase behavior of a porous Ising model with that of a particle-based model for the condensation of methane (CH4) in the isoreticular metal-organic framework IRMOF-16. For both models, we find a line of first-order phase transitions that end in a critical point. We show that the critical behavior in both cases belongs to the 3D Ising universality class, in contrast to other phase transitions in confinement such as capillary condensation.

  4. 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.

  5. Numerically exact correlations and sampling in the two-dimensional Ising spin glass.

    PubMed

    Thomas, Creighton K; Middleton, A Alan

    2013-04-01

    A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest-neighbor spin couplings and then evaluating the Pfaffian of the matrix. Utilizing this technique and other more recent developments in evaluating elements of inverse matrices and exact sampling, a method and computer code for studying two-dimensional Ising models is developed. The formulation of this method is convenient and fast for computing the partition function and spin correlations. It is also useful for exact sampling, where configurations are directly generated with probability given by the Boltzmann distribution. These methods apply to Ising model samples with arbitrary nearest-neighbor couplings and can also be applied to general dimer models. Example results of computations are described, including comparisons with analytic results for the ferromagnetic Ising model, and timing information is provided.

  6. Dynamic phase transition in the two-dimensional kinetic Ising model in an oscillating field: universality with respect to the stochastic dynamics.

    PubMed

    Buendía, G M; Rikvold, P A

    2008-11-01

    We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [Rikvold and Kolesik, J. Phys. A 35, L117 (2002)], for which both nucleation and interface propagation are slower and the interfaces smoother than for the standard Glauber dynamic. We choose the temperature and magnitude of the external field such that the metastable decay of the system following field reversal occurs through nucleation and growth of many droplets of the stable phase, i.e., the multidroplet regime. Using kinetic Monte Carlo simulations, we find that the system undergoes a nonequilibrium phase transition, in which the symmetry-broken dynamic phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. The critical point is located where the half period of the external field is approximately equal to the metastable lifetime of the system. We employ finite-size scaling analysis to investigate the characteristics of this dynamical phase transition. The critical exponents and the fixed-point value of the fourth-order cumulant are found to be consistent with the universality class of the two-dimensional equilibrium Ising model. This universality class has previously been established for the same nonequilibrium model evolving under the standard Glauber dynamic, as well as in a different nonequilibrium model of CO oxidation. The results reported in the present paper support the hypothesis that this far-from-equilibrium phase transition is universal with respect to the choice of the stochastic dynamics.

  7. Nonequilibrium antiferromagnetic mixed-spin Ising model.

    PubMed

    Godoy, Mauricio; Figueiredo, Wagner

    2002-09-01

    We studied an antiferromagnetic mixed-spin Ising model on the square lattice subject to two competing stochastic processes. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip (Glauber dynamics). Besides, the system interacts with an external agency of energy, which supplies energy to it whenever two nearest neighboring spins are simultaneously flipped. By employing Monte Carlo simulations and a dynamical pair approximation, we found the phase diagram for the stationary states of the model in the plane temperature T versus the competition parameter between one- and two-spin flips p. We observed the appearance of three distinct phases, that are separated by continuous transition lines. We also determined the static critical exponents along these lines and we showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.

  8. 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.

  9. Exact interface model for wetting in the planar Ising model

    NASA Astrophysics Data System (ADS)

    Upton, P. J.

    1999-10-01

    At the wetting transition in the two-dimensional Ising model the long contour (interface) gets depinned from the substrate. It is found that on sufficiently large length scales the statistics of the long contour are described by a unique probability measure corresponding to a continuous ``interface model'' with an interface binding ``potential'' given by a Dirac δ function supported on the substrate. A lattice solid-on-solid model is shown to give similar results.

  10. Exact interface model for wetting in the planar Ising model.

    PubMed

    Upton, P J

    1999-10-01

    At the wetting transition in the two-dimensional Ising model the long contour (interface) gets depinned from the substrate. It is found that on sufficiently large length scales the statistics of the long contour are described by a unique probability measure corresponding to a continuous "interface model" with an interface binding "potential" given by a Dirac delta function supported on the substrate. A lattice solid-on-solid model is shown to give similar results.

  11. Conformal symmetry of the critical 3D Ising model inside a sphere

    NASA Astrophysics Data System (ADS)

    Cosme, Catarina; Lopes, J. M. Viana Parente; Penedones, João

    2015-08-01

    We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.

  12. Some Fruits of Genius: Lars Onsager and the Ising Model

    NASA Astrophysics Data System (ADS)

    Fisher, Michael E.

    2006-03-01

    The story of the exact solution of the two-dimensional Ising model by Lars Onsager in the 1940's will be sketched and some of the striking developments following from it, especially for the behavior of fluctuating interfaces, will be recounted.

  13. Dynamical response function of the disordered kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Hinrichsen, Haye

    2008-02-01

    Recently Baumann et al (2007 Preprint 0709.3228v1) studied the phase-ordering kinetics of the two-dimensional Ising model for T

  14. Metastability for the Ising Model on the Hypercube

    NASA Astrophysics Data System (ADS)

    Jovanovski, Oliver

    2017-04-01

    We consider Glauber dynamics for the low-temperature, ferromagnetic Ising Model on the n-dimensional hypercube. We derive precise asymptotic results for the crossover time (the time it takes for the dynamics to go from the configuration with a "-1" at every vertex, to the configuration with a "+1" at each vertex) in the limit as the inverse temperature β → ∞.

  15. Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory.

    PubMed

    Cağlar, Tolga; Berker, A Nihat

    2011-11-01

    The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.

  16. Large Scale Simulations of the Kinetic Ising Model

    NASA Astrophysics Data System (ADS)

    Münkel, Christian

    We present Monte Carlo simulation results for the dynamical critical exponent z of the two- and three-dimensional kinetic Ising model. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems with up to (169984)2 and (3072)3 spins. To our knowledge, these are the largest Ising-systems simulated todate. We also report the successful simulation of very large lattices on a massively parallel MIMD computer with high speedups of approximately 1000 and an efficiency of about 0.93.

  17. Critical region for an Ising model coupled to causal triangulations

    NASA Astrophysics Data System (ADS)

    Cerda-Hernández, J.

    2017-02-01

    This paper extends the results obtained by Hernández et al for the annealed Ising model coupled to two-dimensional causal dynamical triangulations. We employ the Fortuin‑Kasteleyn (FK) representation in order to determine a region in the quadrant of the parameters β,μ >0 where the critical curve for the annealed model is possibly located. This can be done by outlining a region where the model has a unique infinite-volume Gibbs measure, and a region where the finite-volume Gibbs measure does not have weak limit (in fact, does not exist if the volume is large enough). We also improve the region where the model has a one dimensional geometry with respect to the unique weak limit measure, which implies that the Ising model on causal triangulation does not have phase transition in this region. Furthermore, we provide a better approximation of the free energy for the coupled model.

  18. Metastability in an open quantum Ising model.

    PubMed

    Rose, Dominic C; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P

    2016-11-01

    We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.

  19. Metastability in an open quantum Ising model

    NASA Astrophysics Data System (ADS)

    Rose, Dominic C.; Macieszczak, Katarzyna; Lesanovsky, Igor; Garrahan, Juan P.

    2016-11-01

    We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.

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

    PubMed

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

    2016-09-23

    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.

  1. 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

  2. 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.

  3. Dynamical percolation transition in the Ising model studied using a pulsed magnetic field.

    PubMed

    Biswas, Soumyajyoti; Kundu, Anasuya; Chandra, Anjan Kumar

    2011-02-01

    We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature and pulse width and are different from the (static) percolation transition associated with the thermal transition. For a different model that belongs to the Ising universality class, the exponents are found to be same, confirming that the behavior is a common feature of the Ising class. These observations, along with a universal critical Binder cumulant value, characterize the dynamical percolation of the Ising universality class.

  4. Multicritical behavior in dissipative Ising models

    NASA Astrophysics Data System (ADS)

    Overbeck, Vincent R.; Maghrebi, Mohammad F.; Gorshkov, Alexey V.; Weimer, Hendrik

    2017-04-01

    We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady-state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

  5. Ising Model Reprogramming of a Repeat Protein's Equilibrium Unfolding Pathway.

    PubMed

    Millership, C; Phillips, J J; Main, E R G

    2016-05-08

    Repeat proteins are formed from units of 20-40 aa that stack together into quasi one-dimensional non-globular structures. This modular repetitive construction means that, unlike globular proteins, a repeat protein's equilibrium folding and thus thermodynamic stability can be analysed using linear Ising models. Typically, homozipper Ising models have been used. These treat the repeat protein as a series of identical interacting subunits (the repeated motifs) that couple together to form the folded protein. However, they cannot describe subunits of differing stabilities. Here we show that a more sophisticated heteropolymer Ising model can be constructed and fitted to two new helix deletion series of consensus tetratricopeptide repeat proteins (CTPRs). This analysis, showing an asymmetric spread of stability between helices within CTPR ensembles, coupled with the Ising model's predictive qualities was then used to guide reprogramming of the unfolding pathway of a variant CTPR protein. The designed behaviour was engineered by introducing destabilising mutations that increased the thermodynamic asymmetry within a CTPR ensemble. The asymmetry caused the terminal α-helix to thermodynamically uncouple from the rest of the protein and preferentially unfold. This produced a specific, highly populated stable intermediate with a putative dimerisation interface. As such it is the first step in designing repeat proteins with function regulated by a conformational switch.

  6. Dynamical properties of random-field Ising model.

    PubMed

    Sinha, Suman; Mandal, Pradipta Kumar

    2013-02-01

    Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.

  7. Universal dynamic scaling in three-dimensional Ising spin glasses

    NASA Astrophysics Data System (ADS)

    Liu, Cheng-Wei; Polkovnikov, Anatoli; Sandvik, Anders W.; Young, A. P.

    2015-08-01

    We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z =5.85 (9 ) for bimodal couplings distribution and z =6.00 (10 ) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z =5.93 ±0.07 for generic 3D Ising spin glasses.

  8. Ising model of a glass transition.

    PubMed

    Langer, J S

    2013-07-01

    Numerical simulations by Tanaka and co-workers indicate that glass-forming systems of moderately polydisperse hard-core particles, in both two and three dimensions, exhibit diverging correlation lengths. These correlations are described by Ising-like critical exponents, and are associated with diverging, Vogel-Fulcher-Tamann, structural relaxation times. Related simulations of thermalized hard disks indicate that the curves of pressure versus packing fraction for different polydispersities exhibit a sequence of transition points, starting with a liquid-hexatic transition for the monodisperse case, and crossing over with increasing polydispersity to glassy, Ising-like critical points. I propose to explain these observations by assuming that glass-forming fluids contain twofold degenerate, locally ordered clusters of particles, similar to the two-state systems that have been invoked to explain other glassy phenomena. This paper starts with a brief statistical derivation of the thermodynamics of thermalized, hard-core particles. It then discusses how a two-state, Ising-like model can be described within that framework in terms of a small number of statistically relevant, internal state variables. The resulting theory agrees accurately with the simulation data. I also propose a rationale for the observed relation between the Ising-like correlation lengths and the Vogel-Fulcher-Tamann formula.

  9. 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.

  10. Antiferromagnetic Ising Model in Hierarchical Networks

    NASA Astrophysics Data System (ADS)

    Cheng, Xiang; Boettcher, Stefan

    2015-03-01

    The Ising antiferromagnet is a convenient model of glassy dynamics. It can introduce geometric frustrations and may give rise to a spin glass phase and glassy relaxation at low temperatures [ 1 ] . We apply the antiferromagnetic Ising model to 3 hierarchical networks which share features of both small world networks and regular lattices. Their recursive and fixed structures make them suitable for exact renormalization group analysis as well as numerical simulations. We first explore the dynamical behaviors using simulated annealing and discover an extremely slow relaxation at low temperatures. Then we employ the Wang-Landau algorithm to investigate the energy landscape and the corresponding equilibrium behaviors for different system sizes. Besides the Monte Carlo methods, renormalization group [ 2 ] is used to study the equilibrium properties in the thermodynamic limit and to compare with the results from simulated annealing and Wang-Landau sampling. Supported through NSF Grant DMR-1207431.

  11. A sparse Ising model with covariates.

    PubMed

    Cheng, Jie; Levina, Elizaveta; Wang, Pei; Zhu, Ji

    2014-12-01

    There has been a lot of work fitting Ising models to multivariate binary data in order to understand the conditional dependency relationships between the variables. However, additional covariates are frequently recorded together with the binary data, and may influence the dependence relationships. Motivated by such a dataset on genomic instability collected from tumor samples of several types, we propose a sparse covariate dependent Ising model to study both the conditional dependency within the binary data and its relationship with the additional covariates. This results in subject-specific Ising models, where the subject's covariates influence the strength of association between the genes. As in all exploratory data analysis, interpretability of results is important, and we use ℓ1 penalties to induce sparsity in the fitted graphs and in the number of selected covariates. Two algorithms to fit the model are proposed and compared on a set of simulated data, and asymptotic results are established. The results on the tumor dataset and their biological significance are discussed in detail.

  12. Metastable states in homogeneous Ising models

    SciTech Connect

    Achilles, M.; Bendisch, J.; von Trotha, H.

    1987-04-01

    Metastable states of homogeneous 2D and 3D Ising models are studied under free boundary conditions. The states are defined in terms of weak and strict local minima of the total interaction energy. The morphology of these minima is characterized locally and globally on square and cubic grids. Furthermore, in the 2D case, transition from any spin configuration that is not a strict minimum to a strict minimum is possible via non-energy-increasing single flips.

  13. Limiting shapes in two-dimensional Ising ferromagnets.

    PubMed

    Krapivsky, P L; Olejarz, Jason

    2013-06-01

    We consider an Ising model on a square lattice with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution of the interface subject to zero-temperature spin-flip dynamics. We consider an interface which is initially (i) the boundary of the quadrant or (ii) the boundary of a semi-infinite bar. In the former case the interface recedes from its original location in a self-similar diffusive manner. After a rescaling by √[t], the shape of the interface becomes more and more deterministic; we determine this limiting shape analytically and verify our predictions numerically. The semi-infinite bar acquires a stationary shape resembling a finger, and this finger translates along its axis. We compute the limiting shape and the velocity of the Ising finger.

  14. Classical Ising model test for quantum circuits

    NASA Astrophysics Data System (ADS)

    Geraci, Joseph; Lidar, Daniel A.

    2010-07-01

    We exploit a recently constructed mapping between quantum circuits and graphs in order to prove that circuits corresponding to certain planar graphs can be efficiently simulated classically. The proof uses an expression for the Ising model partition function in terms of quadratically signed weight enumerators (QWGTs), which are polynomials that arise naturally in an expansion of quantum circuits in terms of rotations involving Pauli matrices. We combine this expression with a known efficient classical algorithm for the Ising partition function of any planar graph in the absence of an external magnetic field, and the Robertson-Seymour theorem from graph theory. We give as an example a set of quantum circuits with a small number of non-nearest-neighbor gates which admit an efficient classical simulation.

  15. Approaches to numerical solution of 2D Ising model

    NASA Astrophysics Data System (ADS)

    Soldatov, K. S.; Nefedev, K. V.; Kapitan, V. Yu; Andriushchenko, P. D.

    2016-08-01

    Parallel algorithm of partition function calculation of two-dimensional Ising model for systems with a finite number of spins was developed. Within a method of complete enumeration by using MPI technology with subsequent optimization of a parallel code time of calculations was reduced considerably. Partition function was calculated for systems of 16, 25, 36 Ising spins. Based on the obtained results, main thermodynamic and magnetic values dependences (such as heat capacity, magnetic susceptibility, mean square magnetization) for ferromagnetic and antiferromagnetic interactions was investigated. The analysis of a different configurations contribution showed, that states with the minimum energy have essential influence on dependences of thermodynamic values. Comparison with the results obtained by the Wang Landau algorithm was performed.

  16. Spin-correlation function of the fully frustrated Ising model and ± J Ising spin glass on a square lattice

    NASA Astrophysics Data System (ADS)

    M, Y. Ali; J, Poulter

    2013-06-01

    In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.

  17. 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.

  18. 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

  19. Three representations of the Ising model.

    PubMed

    Kruis, Joost; Maris, Gunter

    2016-10-04

    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.

  20. Some results on hyperscaling in the 3D Ising model

    SciTech Connect

    Baker, G.A. Jr.; Kawashima, Naoki

    1995-09-01

    The authors review exact studies on finite-sized 2 dimensional Ising models and show that the point for an infinite-sized model at the critical temperature is a point of nonuniform approach in the temperature-size plane. They also illuminate some strong effects of finite-size on quantities which do not diverge at the critical point. They then review Monte Carlo studies for 3 dimensional Ising models of various sizes (L = 2--100) at various temperatures. From these results they find that the data for the renormalized coupling constant collapses nicely when plotted against the correlation length, determined in a system of edge length L, divided by L. They also find that {zeta}{sub L}/L {ge} 0.26 is definitely too large for reliable studies of the critical value, g*, of the renormalized coupling constant. They have reasonable evidence that {zeta}{sub L}/L {approx} 0.1 is adequate for results that are within one percent of those for the infinite system size. On this basis, they have conducted a series of Monte Carlo calculations with this condition imposed. These calculations were made practical by the development of improved estimators for use in the Swendsen-Wang cluster method. The authors found from these results, coupled with a reversed limit computation (size increases with the temperature fixed at the critical temperature), that g* > 0, although there may well be a sharp downward drop in g as the critical temperature is approached in accord with the predictions of series analysis. The results support the validity of hyperscaling in the 3 dimensional Ising model.

  1. 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.

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

    NASA Astrophysics Data System (ADS)

    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 DM(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 (Tw) versus the magnitude of the crystal field at the middle of the sample (DM), we observe curves of (first-) second-order wetting transitions for (small) high values of DM. Theses lines meet in tricritical wetting points, i.e., (Twtc,DMtc), 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.

  3. 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.

  4. Exact sampling hardness of Ising spin models

    NASA Astrophysics Data System (ADS)

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

    2017-09-01

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

  5. Surface critical behavior of the smoothly inhomogeneous Ising model

    NASA Astrophysics Data System (ADS)

    Burkhardt, Theodore W.; Guim, Ihnsouk

    1984-01-01

    We consider a semi-infinite two-dimensional Ising model with nearest-neighbor coupling constants that deviate from the bulk coupling by Am-y for large m, m being the distance from the edge. The case A<0 of couplings which are weaker near the surface has been discussed by Hilhorst and van Leeuwen. We report exact results for the boundary magnetization and boundary pair-correlation function when A>0. At the bulk critical temperature there is a rich variety of critical behavior in the A -y plane with both paramagnetic and ferromagnetic surface phases. Some of our results can be derived and generalized with simple scaling arguments.

  6. 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.

  7. First excitations in two- and three-dimensional random-field Ising systems

    NASA Astrophysics Data System (ADS)

    Zumsande, M.; Alava, M. J.; Hartmann, A. K.

    2008-02-01

    We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two- and three-dimensional random-field Ising systems with a Gaussian distribution of the random fields. Our algorithm is based on an approach of Frontera and Vives which, in some cases, does not yield the true first excited states. Using the corrected algorithm, we find that the order disorder phase transition for three dimensions is visible via crossings of the excitation energy curves for different system sizes, while in two dimensions these crossings converge to zero disorder. Furthermore, we obtain in three dimensions a fractal dimension of the excitation cluster of ds = 2.42(2). We also provide analytical droplet arguments to understand the behavior of the excitation energies for small and large disorder as well as close to the critical point.

  8. 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.

  9. Nonequilibrium relaxation study of Ising spin glass models

    NASA Astrophysics Data System (ADS)

    Ozeki, Yukiyasu; Ito, Nobuyasu

    2001-07-01

    As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The +/-J Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of L=127 and for four-dimensional (hypercubic) lattice up to L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) Q(t,tw)≡[F], which is a spin correlation of two replicas produced after the waiting time tw from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development (t>>tw) in the SG phase. This provides a reliable upper bound of the transition temperature Tg. It is also found that a scaling relation, Q(t,tw)=t-λqwq¯(t/tw), holds just around the transition point providing the lower bound of Tg. Together with these two bounds, we propose a new dynamical way for the estimation of Tg from much larger systems. In the SG phase, the power-law behavior of the CCF for t>>tw suggests that the SG phase in short-range Ising models has a rugged phase space.

  10. The thermodynamic geometry of the Ising model

    NASA Astrophysics Data System (ADS)

    Rotskoff, Grant; Crooks, Gavin

    2015-03-01

    Biological machines have evolved to produce useful work in a finite time by operating out-of-equilibrium, but we do not know how evolution has guided the design of these machines: Are there generic design principles that direct motors towards higher efficiency? To answer this question, one must first calculate a finite-time efficiency, which poses a significant challenge--tools of equilibrium statistical mechanics fail to describe the relationship between a protocol and the efficiency of a machine subject to that protocol. Using a geometric framework, I will describe a procedure for predicting the protocol that minimizes the dissipated work during an irreversible process. My talk will focus on optimal control of the 2D Ising model; this example will provide strategies for employing geometric thermodynamics to models that cannot be solved analytically.

  11. 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.

  12. Exact Solution of Ising Model in 2d Shortcut Network

    NASA Astrophysics Data System (ADS)

    Shanker, O.

    We give the exact solution to the Ising model in the shortcut network in the 2D limit. The solution is found by mapping the model to the square lattice model with Brascamp and Kunz boundary conditions.

  13. 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. © 2012 American Physical Society

  14. 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.

  15. Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models

    NASA Astrophysics Data System (ADS)

    Binder, Kurt; Luijten, Erik

    2001-04-01

    A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic methodological aspects of these simulations are briefly summarized (single-spin flip vs. cluster algorithms, finite-size scaling concepts), and then the application of these techniques to the nearest-neighbor Ising model in d=3 and 5 dimensions is described, and a detailed comparison to theoretical predictions is made. In addition, the case of Ising models with a large but finite range of interaction and the crossover scaling from mean-field behavior to the Ising universality class are treated. If one considers instead a long-range interaction described by a power-law decay, new classes of critical behavior depending on the exponent of this power law become accessible, and a stringent test of the ε-expansion becomes possible. As a final type of crossover from mean-field type behavior to two-dimensional Ising behavior, the interface localization-delocalization transition of Ising films confined between “competing” walls is considered. This problem is still hampered by questions regarding the appropriate coarse-grained model for the fluctuating interface near a wall, which is the starting point for both this problem and the theory of critical wetting.

  16. GPU-based single-cluster algorithm for the simulation of the Ising model

    NASA Astrophysics Data System (ADS)

    Komura, Yukihiro; Okabe, Yutaka

    2012-02-01

    We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.

  17. Antiferromagnetic Ising model in an imaginary magnetic field

    NASA Astrophysics Data System (ADS)

    Azcoiti, Vicente; Di Carlo, Giuseppe; Follana, Eduardo; Royo-Amondarain, Eduardo

    2017-09-01

    We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual θ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multiprecision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line.

  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. Block renormalization study on the nonequilibrium chiral Ising model.

    PubMed

    Kim, Mina; Park, Su-Chan; Noh, Jae Dong

    2015-01-01

    We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any u<1 exhibiting the power-law scaling of the characteristic length scale ξ∼t(1/z) and the domain-wall density ρ∼t(-δ). The scaling exponents z and δ were found to vary continuously with the parameter u. To establish the anomalous power-law scaling firmly, we perform the block renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.

  20. 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.

  1. The boundary effects of transverse field Ising model

    NASA Astrophysics Data System (ADS)

    He, Yan; Guo, Hao

    2017-09-01

    Advance in quantum simulations using trapped ions or superconducting elements allows detailed analysis of the transverse field Ising model (TFIM), which can exhibit a quantum phase transition and has been a paradigm in exactly solvable quantum systems. The Jordan–Wigner transformation maps the one-dimensional TFIM to a fermion model, but additional complications arise in finite systems and introduce a fermion-number parity constraint when periodic boundary condition is imposed. By constructing the free energy and spin correlations with the fermion-number parity constraint and comparing the results to the TFIM with open boundary condition, we show that the boundary effects can become significant for the anti-ferromagnetic TFIM with odd number of sites at low temperature.

  2. The Planar Ising Model and Total Positivity

    NASA Astrophysics Data System (ADS)

    Lis, Marcin

    2017-01-01

    A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let a_1,dots ,a_k,b_k,dots ,b_1 be vertices placed in a counterclockwise order on the outer face of G. We show that the k× k matrix of the two-point spin correlation functions M_{i,j} = < σ _{a_i} σ _{b_j} rangle is totally nonnegative. Moreover, det M > 0 if and only if there exist k pairwise vertex-disjoint paths that connect a_i with b_i. We also compute the scaling limit at criticality of the probability that there are k parallel and disjoint connections between a_i and b_i in the double random current model. Our results are based on a new distributional relation between double random currents and random alternating flows of Talaska [37].

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

    PubMed

    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 10(3) and 10(6) 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.

  4. 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.

  5. 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

  6. 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

  7. Toward an Ising model of cancer and beyond.

    PubMed

    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

  8. Zero-temperature relaxation of three-dimensional Ising ferromagnets

    NASA Astrophysics Data System (ADS)

    Olejarz, J.; Krapivsky, P. L.; Redner, S.

    2011-05-01

    We investigate the properties of the Ising-Glauber model on a periodic cubic lattice of linear dimension L after a quench to zero temperature. The resulting evolution is extremely slow, with long periods of wandering on constant energy plateaus, punctuated by occasional energy-decreasing spin-flip events. The characteristic time scale τ for this relaxation grows exponentially with the system size; we provide a heuristic and numerical evidence that τ~exp(L2). For all but the smallest-size systems, the long-time state is almost never static. Instead, the system contains a small number of “blinker” spins that continue to flip forever with no energy cost. Thus, the system wanders ad infinitum on a connected set of equal-energy blinker states. These states are composed of two topologically complex interwoven domains of opposite phases. The average genus gL of the domains scales as Lγ, with γ≈1.7; thus, domains typically have many holes, leading to a “plumber’s nightmare” geometry.

  9. On Complexity of the Quantum Ising Model

    NASA Astrophysics Data System (ADS)

    Bravyi, Sergey; Hastings, Matthew

    2017-01-01

    We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local `stoquastic' Hamiltonians with any constant {k ≥ 2}. This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete problem for the complexity class {StoqMA} —an extension of the classical class {MA}. As a corollary, we complete the complexity classification of 2-local Hamiltonians with a fixed set of interactions proposed recently by Cubitt and Montanaro. Secondly, we study quantum annealing algorithms for finding ground states of classical spin Hamiltonians associated with hard optimization problems. We prove that the quantum annealing with TIM Hamiltonians is equivalent modulo polynomial reductions to the quantum annealing with a certain subclass of k-local stoquastic Hamiltonians. This subclass includes all Hamiltonians representable as a sum of a k-local diagonal Hamiltonian and a 2-local stoquastic Hamiltonian.

  10. Droplet model for autocorrelation functions in an Ising ferromagnet

    NASA Technical Reports Server (NTRS)

    Tang, Chao; Nakanishi, Hiizu; Langer, J. S.

    1989-01-01

    The autocorrelation function of Ising spins in an ordered phase is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation which describes fluctuations in the radius of a single droplet is studied in detail. A general description of the transformation to a Fokker-Planck equations and the ways in which a spectral analysis of that equation can be used to compute the autocorrelation function is given. It is shown that the eigenvalues of the Fokker-Planck operator form (1) a continuous spectrum of relaxation rates starting from zero for d = 2, (2) a continuous spectrum with a finite gap for d = 3, and (3) a discrete spectrum for d greater than 4, where d is the spatial dimensionality. Detailed solutions for various cases are presented.

  11. The linear Ising model and its analytic continuation, random walk

    NASA Astrophysics Data System (ADS)

    Lavenda, B. H.

    2004-02-01

    A generalization of Gauss's principle is used to derive the error laws corresponding to Types II and VII distributions in Pearson's classification scheme. Student's r-p.d.f. (Type II) governs the distribution of the internal energy of a uniform, linear chain, Ising model, while the analytic continuation of the uniform exchange energy converts it into a Student t-density (Type VII) for the position of a random walk in a single spatial dimension. Higher-dimensional spaces, corresponding to larger degrees of freedom and generalizations to multidimensional Student r- and t-densities, are obtained by considering independent and identically random variables, having rotationally invariant densities, whose entropies are additive and generating functions are multiplicative.

  12. 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.

  13. 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.

  14. 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.

  15. Long-range transverse Ising model built with dipolar condensates in two-well arrays

    NASA Astrophysics Data System (ADS)

    Li, Yongyao; Pang, Wei; Xu, Jun; Lee, Chaohong; Malomed, Boris A.; Santos, Luis

    2017-01-01

    Dipolar Bose–Einstein condensates in an array of double-well potentials realize an effective transverse Ising model with peculiar inter-layer interactions, that may result under proper conditions in an anomalous first-order ferromagnetic–antiferromagnetic phase transition, and non-trivial phases due to frustration. The considered setup allows as well for the study of Kibble–Zurek defect formation, whose kink statistics follows that expected from the universality class of the mean-field one-dimensional transverse Ising model. Furthermore, random occupation of each layer of the stack leads to random effective Ising interactions and local transverse fields, that may lead to the Anderson-like localization of imbalance perturbations.

  16. Nonperturbative solution of the Ising model on a random surface

    SciTech Connect

    Gross, D.J.; Migdal, A.A. )

    1990-02-12

    The two-matrix-model representation of the Ising model on a random surface is solved exactly to all orders in the genus expansion. The partition function obeys a fourth-order nonlinear differential equation as a function of the string coupling constant. This equation differs from that derived for the {ital k}=3 multicritical one-matrix model, thus disproving that this model describes the Ising model. A similar equation is derived for the Yang-Lee edge singularity on a random surface, and is shown to agree with the {ital k}=3 multicritical one-matrix model.

  17. Ising model for a Brownian donkey

    NASA Astrophysics Data System (ADS)

    Cleuren, B.; Van den Broeck, C.

    2001-04-01

    We introduce a thermal engine consisting of N interacting Brownian particles moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. In response to an external force, absolute negative mobility is observed for N >= 4. For N → ∞ a nonequilibrium phase transition takes place with a spontaneous symmetry breaking entailing the appearance of a current in the absence of an external force.

  18. Linear perturbation renormalization group for the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions in a field

    NASA Astrophysics Data System (ADS)

    Sznajd, J.

    2016-12-01

    The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

  19. Linear perturbation renormalization group for the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions in a field.

    PubMed

    Sznajd, J

    2016-12-01

    The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J) and interchain nearest-neighbor (J_{1}) and next-nearest-neighbor (J_{2}) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J_{2}=-J_{1}/2 for a rectangular lattice and J_{2}=-J_{1} for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.

  20. Self-averaging in the random two-dimensional Ising ferromagnet

    NASA Astrophysics Data System (ADS)

    Dotsenko, Victor; Holovatch, Yurij; Dudka, Maxym; Weigel, Martin

    2017-03-01

    We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ˜L lnln(L ) . In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ peak in the thermodynamic limit L →∞ . While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.

  1. Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field

    NASA Astrophysics Data System (ADS)

    do Nascimento, Denise A.; Pacobahyba, Josefa T.; Neto, Minos A.; Salmon, Octavio D. Rodriguez; Plascak, J. A.

    2017-05-01

    Magnetic phenomena of the two-dimensional anisotropic antiferromagnetic Ising model in both uniform longitudinal (H) and uniform transverse (Ω) magnetic fields are studied by employing a mean-field variational approach based on Bogoliubov inequality for the free energy. The phase diagrams in the magnetic fields and temperature (T) planes, namely H - T and Ω - T, are analyzed on an anisotropic square lattice for some values of the ratio α =Jy /Jx, where Jx and Jy are, respectively, the exchange interactions along the x and y directions. Depending on the range of the Hamiltonian parameters, one has only second-order transition lines, only first-order transition lines, or both first- and second-order transition lines with the presence of tricritical points. In addition, the corresponding phase diagrams are free from any reentrant behavior.

  2. Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination

    NASA Astrophysics Data System (ADS)

    Malakis, A.; Gulpinar, G.; Karaaslan, Y.; Papakonstantinou, T.; Aslan, G.

    2012-03-01

    The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.

  3. Universality of the Ising and the S=1 model on Archimedean lattices: a Monte Carlo determination.

    PubMed

    Malakis, A; Gulpinar, G; Karaaslan, Y; Papakonstantinou, T; Aslan, G

    2012-03-01

    The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.

  4. 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

  5. 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.

  6. Observation of Schramm-Loewner evolution on the geometrical clusters of the Ising model

    NASA Astrophysics Data System (ADS)

    Najafi, M. N.

    2015-05-01

    Schramm-Loewner Evolution (SLE) is a stochastic process that, by focusing on the geometrical features of the two-dimensional (2D) conformal invariant models, classifies them using one real parameter κ. In this work we apply the SLE formalism to the exterior frontiers of the geometrical clusters (interfaces) of the two-dimensional critical Ising model on the triangular lattice. We first analyze the critical curves going from the real axis to the real axis in the upper half plane geometry and show numerically that SLE(κ, κ - 6) works well to extract the diffusivity parameter κ. We then analyze the conformal loops of the critical Ising model. After determining some geometrical exponents of the critical loops as the interfaces of the model in hand, we address the problem of application of SLE to conformal loops. We numerically show that SLE(κ, κ - 6) is more reliable than previous methods.

  7. Heat conduction in one-dimensional aperiodic quantum Ising chains.

    PubMed

    Li, Wenjuan; Tong, Peiqing

    2011-03-01

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

  8. Nonequilibrium random-field Ising model on a diluted triangular lattice.

    PubMed

    Kurbah, Lobisor; Thongjaomayum, Diana; Shukla, Prabodh

    2015-01-01

    We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number z(eff) in the range 3≤z(eff)≤6. We find that the model supports critical behavior in the range 4

  9. Fate of the one-dimensional Ising quantum critical point coupled to a gapless boson

    NASA Astrophysics Data System (ADS)

    Alberton, Ori; Ruhman, Jonathan; Berg, Erez; Altman, Ehud

    2017-02-01

    The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one-dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling renormalization group (RG) indicates a flow toward strong coupling. Using a renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that, depending on the ratio of velocities of the gapless bosonic mode and the Ising critical fluctuations, the transition may remain continuous or become fluctuation-driven first order. The two regimes are separated by a tricritical point of a novel type.

  10. 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.

  11. Phase transitions in Ising models on directed networks.

    PubMed

    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. Domain walls in the quantum transverse Ising model

    NASA Astrophysics Data System (ADS)

    Henkel, Malte; Harris, A. Brooks; Cieplak, Marek

    1995-08-01

    We discuss several problems concerning domain walls in the spin-S Ising model at zero temeprature in a magnetic field, H/(2S), applied in the x direction. Some results are also given for the planar (y-z) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small H and numerically over a large range of H. We obtain the spin-density profile by fixing the spins at opposite ends of the chain to have opposite signs of Sz. One dimensional is special in that there the quantum width of the wall is proportional to the size L of the system. We also study the quantitative features of the ``particle'' band which extends up to energies of order H above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy J/S involving creation of more walls. At large S this particle band develops energy gaps and the lowest subband has tunnel splittings of order H21-2S. This scale of of energy gives rise to anomalous scaling with respect to (a) finite size, (b) temperature, or (c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.

  13. 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.

  14. Red-bond exponents of the critical and the tricritical Ising model in three dimensions

    NASA Astrophysics Data System (ADS)

    Deng, Youjin; Blöte, Henk W. J.

    2004-11-01

    Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p . These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc=1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr=0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr=1/2 for the latter model.

  15. Red-bond exponents of the critical and the tricritical Ising model in three dimensions.

    PubMed

    Deng, Youjin; Blöte, Henk W J

    2004-11-01

    Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p. These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc =1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr =0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr =1/2 for the latter model.

  16. On scaling properties of cluster distributions in Ising models

    NASA Astrophysics Data System (ADS)

    Ruge, C.; Wagner, F.

    1992-01-01

    Scaling relations of cluster distributions for the Wolff algorithm are derived. We found them to be well satisfied for the Ising model in d=3 dimensions. Using scaling and a parametrization of the cluster distribution, we determine the critical exponent β/ν=0.516(6) with moderate effort in computing time.

  17. Ising model on the generalized Bruhat-Tits tree

    NASA Astrophysics Data System (ADS)

    Zinoviev, Yu. M.

    1991-08-01

    The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.

  18. Ising model on the generalized Bruhat-Tits tree

    NASA Astrophysics Data System (ADS)

    Zinoviev, Yu. M.

    1990-06-01

    The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.

  19. The magnetic susceptibility on the transverse antiferromagnetic Ising model: Analysis of the reentrant behavior

    NASA Astrophysics Data System (ADS)

    Neto, Minos A.; de Sousa, J. Ricardo; Padilha, Igor T.; Rodriguez Salmon, Octavio D.; Roberto Viana, J.; Dinóla Neto, F.

    2016-06-01

    We study the three-dimensional antiferromagnetic Ising model in both uniform longitudinal (H) and transverse (Ω) magnetic fields by using the effective-field theory (EFT) with finite cluster N = 1 spin (EFT-1). We analyzed the behavior of the magnetic susceptibility to investigate the reentrant phenomena that we have seen in the same phase diagram previously obtained in other papers. Our results shows the presence of two divergences in the susceptibility that indicates the existence of a reentrant behavior.

  20. Single-cluster algorithm for the site-bond-correlated Ising model

    NASA Astrophysics Data System (ADS)

    Campos, P. R. A.; Onody, R. N.

    1997-12-01

    We extend the Wolff algorithm to include correlated spin interactions in diluted magnetic systems. This algorithm is applied to study the site-bond-correlated Ising model on a two-dimensional square lattice. We use a finite-size scaling procedure to obtain the phase diagram in the temperature-concentration space. We also have verified that the autocorrelation time diminishes in the presence of dilution and correlation, showing that the Wolff algorithm performs even better in such situations.

  1. Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

    We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

  2. 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.

  3. 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.

  4. The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

    NASA Astrophysics Data System (ADS)

    Merdan, Z.; Güzelsoy, E.

    2012-05-01

    The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤ L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T c (∞)=6.6788(65), T c (∞)=6.6798(69), T c (∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤ L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T c (∞)=6.6817(15), T c (∞)=6.6802(2), the dynamic Monte Carlo result of T c (∞)=6.6803(1), the cluster Monte Carlo result of T c (∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T c (∞)=6.6802632±5×10-5.

  5. Zero- and low-temperature behavior of the two-dimensional ±J Ising spin glass.

    PubMed

    Thomas, Creighton K; Huse, David A; Middleton, A Alan

    2011-07-22

    Scaling arguments and precise simulations are used to study the square lattice ±J Ising spin glass, a prototypical model for glassy systems. Droplet theory explains, and our numerical results show, entropically stabilized long-range spin-glass order at zero temperature, which resembles the energetic stabilization of long-range order in higher-dimensional models at finite temperature. At low temperature, a temperature-dependent crossover length scale is used to predict the power-law dependence on temperature of the heat capacity and clarify the importance of disorder distributions.

  6. Velocity-space synthesis of ISEE-1 measurements of the three dimensional electron distribution function

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

    A computer package which produces contour plots of the three dimensional electron distribution function measured by an electron spectrometer aboard ISEE-1 is described. Examples of the contour plots and an explanation of how to use the program, including the necessary computer code for running the program on the GSFC 360/91 computer is presented. The method by which the discrete measurements of the distribution function, given by points on the four dimensional surface are synthesized into a smooth surface in a three dimensional space which can be contoured is described. The velocity components are parallel and perpendicular to the magnetic field, respectively, in the proper frame of the electrons.

  7. Frustrated Ising model on the Cairo pentagonal lattice.

    PubMed

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

    2012-11-01

    Through the direct decoration transformation approach, we obtain a general solution for the pentagonal Ising model, showing its equivalence to the isotropic free-fermion eight-vertex model. We study the ground-state phase diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state, and one frustrated state are found. Using the exact solution of the pentagonal Ising model, we discuss the finite-temperature phase diagrams and find a phase transition between the FIM state and the disordered state as well as a phase transition between the disordered state and the FM state. We also discuss some additional remarkable properties of the model, such as the magnetization, entropy, and specific heat, at finite temperature and at its low-temperature asymptotic limit. Because of the influence of the second-order phase transition between the frustrated and ferromagnetic phases, we obtain surprisingly low values of the entropy and the specific heat until the critical temperature is reached.

  8. Kallen Lehman approach to 3D Ising model

    NASA Astrophysics Data System (ADS)

    Canfora, F.

    2007-03-01

    A “Kallen-Lehman” approach to Ising model, inspired by quantum field theory à la Regge, is proposed. The analogy with the Kallen-Lehman representation leads to a formula for the free-energy of the 3D model with few free parameters which could be matched with the numerical data. The possible application of this scheme to the spin glass case is shortly discussed.

  9. 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.

  10. Critical dynamics of cluster algorithms in the dilute Ising model

    NASA Astrophysics Data System (ADS)

    Hennecke, M.; Heyken, U.

    1993-08-01

    Autocorrelation times for thermodynamic quantities at T C are calculated from Monte Carlo simulations of the site-diluted simple cubic Ising model, using the Swendsen-Wang and Wolff cluster algorithms. Our results show that for these algorithms the autocorrelation times decrease when reducing the concentration of magnetic sites from 100% down to 40%. This is of crucial importance when estimating static properties of the model, since the variances of these estimators increase with autocorrelation time. The dynamical critical exponents are calculated for both algorithms, observing pronounced finite-size effects in the energy autocorrelation data for the algorithm of Wolff. We conclude that, when applied to the dilute Ising model, cluster algorithms become even more effective than local algorithms, for which increasing autocorrelation times are expected.

  11. Ising anyons in frustration-free Majorana-dimer models

    NASA Astrophysics Data System (ADS)

    Ware, Brayden; Son, Jun Ho; Cheng, Meng; Mishmash, Ryan V.; Alicea, Jason; Bauer, Bela

    2016-09-01

    Dimer models have long been a fruitful playground for understanding topological physics. Here, we introduce a class, termed Majorana-dimer models, wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological px-i py superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the Ising×(px-i py) theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.

  12. Information cascade, Kirman's ant colony model, and kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Hisakado, Masato; Mori, Shintaro

    2015-01-01

    In this paper, we discuss a voting model in which voters can obtain information from a finite number of previous voters. There exist three groups of voters: (i) digital herders and independent voters, (ii) analog herders and independent voters, and (iii) tanh-type herders. In our previous paper Hisakado and Mori (2011), we used the mean field approximation for case (i). In that study, if the reference number r is above three, phase transition occurs and the solution converges to one of the equilibria. However, the conclusion is different from mean field approximation. In this paper, we show that the solution oscillates between the two states. A good (bad) equilibrium is where a majority of r select the correct (wrong) candidate. In this paper, we show that there is no phase transition when r is finite. If the annealing schedule is adequately slow from finite r to infinite r, the voting rate converges only to the good equilibrium. In case (ii), the state of reference votes is equivalent to that of Kirman's ant colony model, and it follows beta binomial distribution. In case (iii), we show that the model is equivalent to the finite-size kinetic Ising model. If the voters are rational, a simple herding experiment of information cascade is conducted. Information cascade results from the quenching of the kinetic Ising model. As case (i) is the limit of case (iii) when tanh function becomes a step function, the phase transition can be observed in infinite size limit. We can confirm that there is no phase transition when the reference number r is finite.

  13. Cluster algorithms for frustrated two-dimensional Ising antiferromagnets via dual worm constructions

    NASA Astrophysics Data System (ADS)

    Rakala, Geet; Damle, Kedar

    2017-08-01

    We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbors on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbor couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wave vector.

  14. 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.

  15. Combinatorial approach to exactly solve the 1D Ising model

    NASA Astrophysics Data System (ADS)

    Seth, Swarnadeep

    2017-01-01

    The Ising model is a well known statistical model which can be solved exactly by various methods. The most familiar one is the transfer matrix method. Sometimes it can be difficult to approach the open boundary case rather than periodic boundary ones in higher dimensions. But physically it is more intuitive to study the open boundary case, as it gives a closer view of the real system. We have introduced a new method called the pairing method to determine the exact partition function for the simplest case, a 1D Ising lattice. This method simplifies the problem's complexities and reduces it to a pure combinatorial problem. The study also reveals that it is possible to apply this pairing method in the case of a 2D square lattice. The obtained results agree perfectly with the values in the literature and this new approach provides an algorithmic insight to deal with such problems.

  16. A Binomial Approximation Method for the Ising Model

    NASA Astrophysics Data System (ADS)

    Streib, Noah; Streib, Amanda; Beichl, Isabel; Sullivan, Francis

    2014-08-01

    A large portion of the computation required for the partition function of the Ising model can be captured with a simple formula. In this work, we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the Ising model that requires no algorithm at all. This approximation, which uses the high temperature expansion, is solely based on the binomial distribution, and performs very well at low temperatures. At high temperatures, we provide an alternative approximation, which also serves as a lower bound on the partition function and is trivial to compute. We provide theoretical evidence and the results of numerical experiments to support the strength of these approximations.

  17. Critical exponents for the 3D Ising model

    SciTech Connect

    Gupta, R.; Tamayo, P. |

    1996-03-01

    The authors present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 64{sup 3}, 128{sup 3}, and 256{sup 3} simple cubic lattices. Their MCRG estimates are K{sup c}{sub nn} = 0.221655(1)(1) and {nu} = 0.625(1). The FSS results for K{sup c} are consistent with those from MCRG but the value of {nu} is not. Their best estimate {eta} = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of their calculation is the estimate {omega} {approx} 0.7 for the correction-to-scaling exponent. The authors also present results for the renormalized coupling g{sub R} along the MCRG flow and argue that the data supports the validity of hyperscaling for the 3D Ising model.

  18. Critical Casimir forces between defects in the 2D Ising model

    NASA Astrophysics Data System (ADS)

    Nowakowski, P.; Maciołek, A.; Dietrich, S.

    2016-12-01

    An exact statistical mechanical derivation is given of the critical Casimir interactions between two defects in a planar lattice-gas Ising model. Each defect is a finite group of nearest-neighbor spins with modified coupling constants. Such a system can be regarded as a model of a binary liquid mixture with the molecules confined to a membrane and the defects mimicking protein inclusions embedded into the membrane. As suggested by recent experiments, certain cellular membranes appear to be tuned to the proximity of a critical demixing point belonging to the two-dimensional Ising universality class. Therefore one can expect the emergence of critical Casimir forces between membrane inclusions. These forces are governed by universal scaling functions, which we derive for simple defects. We prove that the scaling law appearing at criticality is the same for all types of defects considered here.

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

    PubMed

    Deng, Zehui; Wu, Jinshan; Guo, Wenan

    2014-12-01

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

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

    NASA Astrophysics Data System (ADS)

    Deng, Zehui; Wu, Jinshan; Guo, Wenan

    2014-12-01

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

  1. 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.

  2. Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

    NASA Astrophysics Data System (ADS)

    Salas, J.

    1995-09-01

    A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.

  3. 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.

  4. Ground state nonuniversality in the random-field Ising model

    SciTech Connect

    Duxbury, P. M.; Meinke, J. H.

    2001-09-01

    Two attractive and often used ideas, namely, universality and the concept of a zero-temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are nonuniversal. However, we also show that at finite temperature the thermal order-parameter exponent 1/2 is restored so that temperature is a relevant variable. Broader implications of these results are discussed.

  5. Genus-two characters of the Ising model

    NASA Astrophysics Data System (ADS)

    Choi, J. H.; Koh, I. G.

    1989-05-01

    As a first step in studying conformal theories on a higher-genus Riemann surface, we construct genus-two characters of the Ising model from their behavior in zero- and nonzero-homology pinching limits, the Goddard-Kent-Olive coset-space construction, and the branching coefficients in the level-two A(1)1 Kac-Moody characters on the higher-genus Riemann surface.

  6. Repairing Stevenson's step in the 4d Ising model

    NASA Astrophysics Data System (ADS)

    Balog, Janos; Niedermayer, Ferenc; Weisz, Peter

    2006-05-01

    In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved statistics and show that the results are indeed consistent with conventional wisdom once one takes into account the uncertainty of lattice artifacts in the analytical computations.

  7. Lateral critical Casimir force in two-dimensional inhomogeneous Ising strip. Exact results.

    PubMed

    Nowakowski, Piotr; Napiórkowski, Marek

    2016-06-07

    We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to +h1 except for a group of N1 neighboring surface spins where it is equal to -h1. The inhomogeneities of the upper and lower wall are shifted with respect to each other by a lateral distance L. Using exact diagonalization of the transfer matrix, we study both the lateral and normal critical Casimir forces as well as magnetization profiles for different temperature regimes: below the wetting temperature, between the wetting and the critical temperature, and above the critical temperature. The lateral critical Casimir force acts in the direction opposite to the shift L, and the excess normal force is always attractive. Upon increasing the shift L we observe, depending on the temperature regime, three different scenarios of breaking of the capillary bridge of negative magnetization connecting the inhomogeneities of the walls across the strip. As long as there exists a capillary bridge in the system, the magnitude of the excess total critical Casimir force is almost constant, with its direction depending on L. By investigating the bridge morphologies we have found a relation between the point at which the bridge breaks and the inflection point of the force. We provide a simple argument that some of the properties reported here should also hold for different models of the strip with the same type of inhomogeneity.

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

    NASA Astrophysics Data System (ADS)

    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 Tw 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 Tw from below are studied. In accord with theoretical predictions, for T >Tw 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 (b1 /2). So, the area of the droplet is proportional to b3 /2, and the temperature dependence of the corresponding prefactor, which also involves the interfacial stiffness, is studied.

  10. 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.

  11. Critical behavior of the quantum Ising model on a fractal structure.

    PubMed

    Yi, Hangmo

    2013-07-01

    We study the critical behavior of the transverse-field quantum Ising model on a fractal structure, namely the Sierpinski carpet. When a magnetic field Δ is applied perpendicular to the Ising spin direction, quantum fluctuations affect the transition between the ferromagnetic and the paramagnetic phases. Employing the continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, we investigate the interplay between the quantum fluctuations and the exotic dimensionality of the fractal structure and its effect on the critical behavior. As the transverse magnetic field increases, the critical temperature monotonically decreases until it apparently vanishes at a critical field Δ(c), beyond which the system becomes paramagnetic at all temperatures. However, the critical exponents are independent of Δ and remain the same as in the purely classical(Δ=0) case.

  12. Interface localization in the 2D Ising model with a driven line

    NASA Astrophysics Data System (ADS)

    Cohen, O.; Mukamel, D.

    2016-04-01

    We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is ‘stronger’ than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.

  13. A new molecular thermodynamic model for multicomponent Ising lattice

    NASA Astrophysics Data System (ADS)

    Yang, Jianyong; Xin, Qin; Sun, Lei; Liu, Honglai; Hu, Ying; Jiang, Jianwen

    2006-10-01

    A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.

  14. Simulating the Rayleigh-Taylor instability with the Ising model

    SciTech Connect

    Ball, Justin R.; Elliott, James B.

    2011-08-26

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

  15. 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.

  16. Multi-GPU accelerated multi-spin Monte Carlo simulations of the 2D Ising model

    NASA Astrophysics Data System (ADS)

    Block, Benjamin; Virnau, Peter; Preis, Tobias

    2010-09-01

    A Modern Graphics Processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two-dimensional Ising model [T. Preis et al., Journal of Chemical Physics 228 (2009) 4468-4477] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.

  17. 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.

  18. Defects in the tri-critical Ising model

    NASA Astrophysics Data System (ADS)

    Makabe, Isao; Watts, Gérard M. T.

    2017-09-01

    We consider two different conformal field theories with central charge c = 7 /10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c = 7 /5, using the folding trick as first proposed by Gang and Yamaguchi [1]. We then act on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.

  19. Real-space renormalization group for the transverse-field Ising model in two and three dimensions.

    PubMed

    Miyazaki, Ryoji; Nishimori, Hidetoshi; Ortiz, Gerardo

    2011-05-01

    The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.

  20. Replica exchange simulations of the three-dimensional Ising spin glass: static and dynamic properties

    NASA Astrophysics Data System (ADS)

    Yucesoy, Burcu; Machta, Jonathan; Katzgraber, Helmut G.

    2012-02-01

    We present the results of a large-scale numerical study of the equilibrium three-dimensional Ising spin glass with Gaussian disorder. Using replica exchange (parallel tempering) Monte Carlo, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the replica exchange Monte Carlo method. The correlation between static and dynamic observables for 5000 disorder realizations (N <=10^3 spins) down to very low temperatures (T 0.2Tc) is examined. Our results show that autocorrelation times are directly correlated with the roughness of the free energy landscape. We also discuss the size dependence of several static quantities.

  1. Restricted Boltzmann machines for the long range Ising models

    NASA Astrophysics Data System (ADS)

    Aoki, Ken-Ichi; Kobayashi, Tamao

    2016-12-01

    We set up restricted Boltzmann machines (RBM) to reproduce the long range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of configuration with probability (CwP). The quality of resultant RBM is evaluated through the susceptibility with respect to the magnetic external field. We compare the results with those by block decimation renormalization group (BDRG) method, and our RBM clear the test with satisfactory precision.

  2. Creep motion in a random-field Ising model.

    PubMed

    Roters, L; Lübeck, S; Usadel, K D

    2001-02-01

    We analyze numerically a moving interface in the random-field Ising model which is driven by a magnetic field. Without thermal fluctuations the system displays a depinning phase transition, i.e., the interface is pinned below a certain critical value of the driving field. For finite temperatures the interface moves even for driving fields below the critical value. In this so-called creep regime the dependence of the interface velocity on the temperature is expected to obey an Arrhenius law. We investigate the details of this Arrhenius behavior in two and three dimensions and compare our results with predictions obtained from renormalization group approaches.

  3. Ising model simulation in directed lattices and networks

    NASA Astrophysics Data System (ADS)

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

    2006-01-01

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

  4. 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.

  5. Interfaces in driven Ising models: shear enhances confinement.

    PubMed

    Smith, Thomas H R; Vasilyev, Oleg; Abraham, Douglas B; Maciołek, Anna; Schmidt, Matthias

    2008-08-08

    We use a phase-separated driven two-dimensional Ising lattice gas to study fluid interfaces exposed to shear flow parallel to the interface. The interface is stabilized by two parallel walls with opposing surface fields, and a driving field parallel to the walls is applied which (i) either acts locally at the walls or (ii) varies linearly with distance across the strip. Using computer simulations with Kawasaki dynamics, we find that the system reaches a steady state in which the magnetization profile is the same as that in equilibrium, but with a rescaled length implying a reduction of the interfacial width. An analogous effect was recently observed in sheared phase-separated colloidal dispersions. Pair correlation functions along the interface decay more rapidly with distance under drive than in equilibrium and for cases of weak drive, can be rescaled to the equilibrium result.

  6. Accelerated rare event sampling: Refinement and Ising model analysis

    NASA Astrophysics Data System (ADS)

    Yevick, David; Lee, Yong Hwan

    In this paper, a recently introduced accelerated sampling technique [D. Yevick, Int. J. Mod. Phys. C 27, 1650041 (2016)] for constructing transition matrices is further developed and applied to a two-dimensional 32×32 Ising spin system. By permitting backward displacements up to a certain limit for each forward step while evolving the system to first higher and then lower energies within a restricted interval that is steadily displaced toward zero temperature as the computation proceeds, accuracy can be greatly enhanced. Simultaneously, the elements obtained from numerous independent calculations are collected in a single transition matrix. The relative accuracy of this novel method is established through a comparison to a transition matrix procedure based on the Metropolis algorithm in which the temperature is appropriately varied during the calculation and the results interpreted in terms of the distribution of realizations over both energy and magnetization.

  7. 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

  8. Rare events in a finite 2D Ising model

    NASA Astrophysics Data System (ADS)

    Xuan, Ning

    The dynamics of physical systems are always subject to thermal fluctuations or noise. These perturbations will make the stable states of the deterministic part of the dynamical system become only metastable states. When the amplitude of the perturbation is small, the transitions from one metastable state to another are rare events. One such example is the magnetization switching between the two metastable states of 2D Ising model at T < Tc. The 2D Ising model displays two metastable states below the critical temperature Tc. These metastable states are characterized by spontaneous magnetization per spin that tend to m = +/-1 as temperature T → 0. A finite-size Ising system performs transitions from one metastable phase to another due to thermal fluctuations. Such phase transitions often involve growth or birth of a thermally activated critical nucleus, which is statistically a rare event when the noise is small. It may occur via homogeneous nucleation or heterogeneous nucleation, depending on whether the nucleus is formed in system with periodic boundary condition or with boundary condition of Dirichlet or Neumann type. In this thesis, we study the influences of an applied bulk field and local boundary fields to the critical points (minimums and saddle) of noised-driven phase transitions arising in a finite 2D Ising system in both frameworks of the Ginzburg-Landau theory and lattice spins. We use the string method to numerically allocate the minimum energy path (MEP) and the profile of the energy barrier along it. In the framework of Ginzburg-Landau, we introduce an interface energy functional as a sharp interface limit of the Ginzburg-Landau energy, and compare the numerical results from the string method to the analytical results from this interface energy. In the framework of lattice spin model, we first applied the Transition Path Theory to the system to get the transition rate functional that is suitable for both theoretical and numerical purpose. Then the

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

    NASA Astrophysics Data System (ADS)

    Herdeiro, Victor

    2017-09-01

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

  10. Generic phase coexistence in the totally asymmetric kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Godrèche, Claude; Luck, Jean-Marc

    2017-07-01

    The physical analysis of generic phase coexistence in the North-East-Center Toom model was originally given by Bennett and Grinstein. The gist of their argument relies on the dynamics of interfaces and droplets. We revisit the same question for a specific totally asymmetric kinetic Ising model on the square lattice. This nonequilibrium model possesses the remarkable property that its stationary-state measure in the absence of a magnetic field coincides with that of the usual ferromagnetic Ising model. We use both analytical arguments and numerical simulations in order to make progress in the quantitative understanding of the phenomenon of generic phase coexistence. At zero temperature a mapping onto the TASEP allows an exact determination of the time-dependent shape of the ballistic interface sweeping a large square minority droplet of up or down spins. At finite temperature, measuring the mean lifetime of such a droplet allows an accurate measurement of its shrinking velocity v, which depends on temperature T and magnetic field h. In the absence of a magnetic field, v vanishes with an exponent Δ_v≈2.5+/-0.2 as the critical temperature T c is approached. At fixed temperature in the ordered phase, v vanishes at the phase-boundary fields +/- h_b(T) which mark the limits of the coexistence region. The latter fields vanish with an exponent Δ_h≈3.2+/-0.3 as T c is approached.

  11. 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.

  12. Investigation of probability theory on Ising models with different four-spin interactions

    NASA Astrophysics Data System (ADS)

    Yang, Yuming; Teng, Baohua; Yang, Hongchun; Cui, Haijuan

    2017-10-01

    Based on probability theory, two types of three-dimensional Ising models with different four-spin interactions are studied. Firstly the partition function of the system is calculated by considering the local correlation of spins in a given configuration, and then the properties of the phase transition are quantitatively discussed with series expansion technique and numerical method. Meanwhile the rounding errors in this calculation is analyzed so that the possibly source of the error in the calculation based on the mean field theory is pointed out.

  13. From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

    NASA Astrophysics Data System (ADS)

    de Tilière, Béatrice

    2013-04-01

    Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph G and the dimer model defined on a decorated version {{G}} of this graph (Fisher in J Math Phys 7:1776-1781, 1966). In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain {{G}_1}. Our main result consists in explicitly constructing CRSFs of {{G}_1} counted by the dimer characteristic polynomial, from CRSFs of G 1, where edges are assigned Kenyon's critical weight function (Kenyon in Invent Math 150(2):409-439, 2002); thus proving a relation on the level of configurations between two well known 2-dimensional critical models.

  14. 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.

  15. Dual time scales in simulated annealing of a two-dimensional Ising spin glass.

    PubMed

    Rubin, Shanon J; Xu, Na; Sandvik, Anders W

    2017-05-01

    We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼L^{z}, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent z_{eq}(T), for which previous studies have found a divergent behavior: z_{eq}(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.

  16. Dual time scales in simulated annealing of a two-dimensional Ising spin glass

    NASA Astrophysics Data System (ADS)

    Rubin, Shanon J.; Xu, Na; Sandvik, Anders W.

    2017-05-01

    We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T =0 of the two-dimensional Ising model with random J =±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ ˜Lz , are z =8.28 ±0.03 for the relaxation of the order parameter and z =10.31 ±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T →0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent zeq(T ) , for which previous studies have found a divergent behavior: zeq(T →0 ) →∞ . Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.

  17. 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)

  18. 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

  19. The Ising Model Applied on Chronification of Pain.

    PubMed

    Granan, Lars-Petter

    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.

  20. Quantum dimensions from local operator excitations in the Ising model

    NASA Astrophysics Data System (ADS)

    Caputa, Paweł; Rams, Marek M.

    2017-02-01

    We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Rényi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.

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

    PubMed

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

    2011-10-01

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

  2. Ising models on the 2 x 2 x {infinity} lattices

    SciTech Connect

    Yurishchev, M. A.

    2007-03-15

    Exact analytic solutions are presented for two 2 x 2 x {infinity} Ising etageres. The first model has a simple cubic lattice with fully anisotropic interactions. The second model consists of two different types of linear chains and includes noncrossing diagonal bonds on the side faces of the 2 x 2 x {infinity} parallelepiped. In both cases, the solutions are expressed through square radicals and obtained by using the obvious symmetry of the Hamiltonians, Z{sub 2} x C{sub 2v}, and the hidden algebraic {lambda}{lambda} symmetry of the transfer matrix secular equations. The solution found for the second model is used to analyze the behavior of specific heat in a frustrated many-chain system.

  3. Propagation of fluctuations in the quantum Ising model

    NASA Astrophysics Data System (ADS)

    Navez, P.; Tsironis, G. P.; Zagoskin, A. M.

    2017-02-01

    We investigate entanglement dynamics and correlations in the quantum Ising model in arbitrary dimensions using a large-coordination-number expansion. We start from the pure paramagnetic regime obtained through zero spin-spin coupling and subsequently turn on the interspin interaction in a time-dependent fashion. We investigate analytically and compare results for both the slow adiabatic onset of the interactions and the fast instantaneous switching. We find that in the latter case of an initial excitation mode a quantum correlation wave spreads through the system, propagating with twice the group velocity of the linearized equilibrium modes. This wave establishes the spatiotemporal regime of entangled quantum properties of the system for time scales shorter than the decoherence time and thus provides an indicator for the "quantumness" of the physical system that the specific system models.

  4. Maximum Likelihood Reconstruction for Ising Models with Asynchronous Updates

    NASA Astrophysics Data System (ADS)

    Zeng, Hong-Li; Alava, Mikko; Aurell, Erik; Hertz, John; Roudi, Yasser

    2013-05-01

    We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases: one in which we know both the spin history and the update times and one in which we know only the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be derived within a further decoupling approximation. We study all methods numerically for fully asymmetric Sherrington-Kirkpatrick models, varying the data length, system size, temperature, and external field. Good convergence is observed in accordance with the theoretical expectations.

  5. Ising model with short-range correlated dilution

    NASA Astrophysics Data System (ADS)

    Branco, N. S.; de Queiroz, S. L. A.; Dos Santos, Raimundo R.

    1988-07-01

    We consider a diluted Ising model in which the absence of a spin affects the exchange coupling of a nearest-neighbor pair along the line joining the three spins; that is, it aquires the value αJ, where α is a phenomenological parameter ɛ[0,1]. This model has been proposed to explain the experimental phase diagram for KNixMg1-xF3. A position-space renormalization-group analysis clearly distinguishes two percolation thresholds depending on whether α=0 or α>0, though both cases seem to be in the same universality class. Further, thermal fluctuations dominate over the geometrical ones as in the uncorrelated case and the critical curve (critical temperature versus concentration of magnetic sites) displays an upward curvature for intermediate degrees of correlation 0<α<1, as experimentally observed.

  6. 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.

  7. Critical behavior of the mixed-spin Ising model with two competing dynamics.

    PubMed

    Godoy, Mauricio; Figueiredo, Wagner

    2002-02-01

    In this work we investigate the stationary states of a nonequilibrium mixed-spin Ising model on a square lattice. The model system consists of two interpenetrating sublattices of spins sigma=1/2 and S=1, and we take only nearest neighbor interactions between pairs of spins. The system is in contact with a heat bath at temperature T and subject to an external flux of energy. The contact with the heat bath is simulated by single spin flips according to the Metropolis rule, while the input of energy is mimicked by the simultaneous flipping of pairs of neighboring spins. We performed Monte Carlo simulations on this model in order to find its phase diagram in the plane of temperature T versus the competition parameter between one- and two-spin flips, p. The phase diagram of the model exhibits two ordered phases with sublattice magnetizations m(1), m(2)>0 and m(1)>0, m(2)<0. These phases are separated from the paramagnetic phase (m(1)=m(2)=0) by continuous transition lines. We found the static critical exponents along these lines and showed that this nonequilibrium model belongs to the universality class of the two-dimensional equilibrium Ising model.

  8. 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.

  9. Maximum caliber inference and the stochastic Ising model

    NASA Astrophysics Data System (ADS)

    Cafaro, Carlo; Ali, Sean Alan

    2016-11-01

    We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.

  10. Hysteresis in an Ising model with mobile bonds

    NASA Astrophysics Data System (ADS)

    Čapeta, D.; Sunko, D. K.

    2005-04-01

    Hysteresis is studied in a disordered Ising model in which diffusion of antiferromagnetic bonds is allowed in addition to spin flips. Saturation behavior changes to a figure-eight loop when diffusion is introduced. The upper and lower fields delimiting the figure-eight are determined by the Hamiltonian, while its surface and the crossing point depend on the temperature and details of the dynamics. The main avalanche is associated with the disappearance of hidden order. Some experimental observations of figure-eight anomalies are discussed. It is argued they are a signal of a transient rearrangement of domain couplings, characteristic of amorphous and/or magnetically soft samples, and similar to evolution of kinetic glasses.

  11. Double resonance in the infinite-range quantum Ising model.

    PubMed

    Han, Sung-Guk; Um, Jaegon; Kim, Beom Jun

    2012-08-01

    We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the z direction is performed at various transverse field strengths g. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of g, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.

  12. Maximum caliber inference and the stochastic Ising model.

    PubMed

    Cafaro, Carlo; Ali, Sean Alan

    2016-11-01

    We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.

  13. Robust criticality of an Ising model on rewired directed networks.

    PubMed

    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.

  14. Critical thermodynamics of the two-dimensional +/-J Ising spin glass.

    PubMed

    Lukic, J; Galluccio, A; Marinari, E; Martin, O C; Rinaldi, G

    2004-03-19

    We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an "effective" gap of size 2J; in addition, an associated crossover length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low lying excitations and by the way low energy domain walls proliferate in this model.

  15. Nonequilibrium variational cluster perturbation theory: Quench dynamics of the quantum Ising model

    NASA Astrophysics Data System (ADS)

    Asadzadeh, Mohammad Zhian; Fabrizio, Michele; Arrigoni, Enrico

    2016-11-01

    We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional case, for which we have to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic timescale τ that increases with the size of the cluster used for CPT. In addition, and not surprisingly, τ is small for quenches across the equilibrium phase transition point, but can be quite larger for quenches within the ordered or disordered phases.

  16. Conformal invariance and stochastic Loewner evolution processes in two-dimensional Ising spin glasses.

    PubMed

    Amoruso, C; Hartmann, A K; Hastings, M B; Moore, M A

    2006-12-31

    We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with kappa approximately 2.1. An argument is given that their fractal dimension d(f) is related to their interface energy exponent theta by d(f) - 1 = 3/[4(3 + theta)], which is consistent with the commonly quoted values d(f) approximately 1.27 and theta approximately -0.28.

  17. Conformal Invariance and Stochastic Loewner Evolution Processes in Two-Dimensional Ising Spin Glasses

    SciTech Connect

    Amoruso, C.; Moore, M. A.; Hartmann, A. K.; Hastings, M. B.

    2006-12-31

    We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with {kappa}{approx_equal}2.1. An argument is given that their fractal dimension d{sub f} is related to their interface energy exponent {theta} by d{sub f}-1=3/[4(3+{theta})], which is consistent with the commonly quoted values d{sub f}{approx_equal}1.27 and {theta}{approx_equal}-0.28.

  18. Thermodynamics and Phase Transitions of Ising Model on Inhomogeneous Stochastic Recursive Lattice

    NASA Astrophysics Data System (ADS)

    Huang, Ran

    As one of the few exactly solvable thermodynamic models, the Ising model on recursive lattice is featured by its impressive advantages and successful applications in various thermodynamic and statistical researches. However this model was considered that, since the recursive calculation demands homogeneous structure, it can only describe the bulk and even systems with narrow utilization. In this work we figured out a practical methodology to extend the conventional homogeneous structure of single-unit Husimi lattice to be random inhomogeneous lattices with variable units and structures, while keeping the feature of exact calculation. Three designs of inhomogeneous recursive lattices: the random-angled rhombus lattice, the Husimi lattice of variable units, and the randomly multi-branched Husimi square lattice; and the corresponding exact recursive calculations based on the partial partition function algorithm, which is derived from the Bethe Cavity method, have been investigated and developed. With the ``total-symmetry assumption'' and the ``iterative-replica trick'' we were able to exactly solve the classical ferromagnetic spin-1 Ising models on these lattices, to describe the complex systems that can only be solved by approximations or simulations on regular lattices. Our work may enhance the application of the exact calculation on recursive lattices in various fields of materials science and applied physics, especially it may serve as a powerful tool to explore the cross-dimensional thermodynamics and phase transitions. National Natural Science Foundation of China (Grant No. 11505110).

  19. Completeness of the classical 2D Ising model and universal quantum computation.

    PubMed

    Van den Nest, M; Dür, W; Briegel, H J

    2008-03-21

    We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.

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

    SciTech Connect

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

    2016-10-01

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

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

    DOE PAGES

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

    2016-10-01

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

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

    SciTech Connect

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

    2016-10-01

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

  3. Emergent 1d Ising Behavior in AN Elementary Cellular Automaton Model

    NASA Astrophysics Data System (ADS)

    Kassebaum, Paul G.; Iannacchione, Germano S.

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

  4. Stochastic bifurcations in the nonlinear parallel Ising model.

    PubMed

    Bagnoli, Franco; Rechtman, Raúl

    2016-11-01

    We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

  5. Stochastic bifurcations in the nonlinear parallel Ising model

    NASA Astrophysics Data System (ADS)

    Bagnoli, Franco; Rechtman, Raúl

    2016-11-01

    We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

  6. Ising percolation in a three-state majority vote model

    NASA Astrophysics Data System (ADS)

    Balankin, Alexander S.; Martínez-Cruz, M. A.; Gayosso Martínez, Felipe; Mena, Baltasar; Tobon, Atalo; Patiño-Ortiz, Julián; Patiño-Ortiz, Miguel; Samayoa, Didier

    2017-02-01

    In this Letter, we introduce a three-state majority vote model in which each voter adopts a state of a majority of its active neighbors, if exist, but the voter becomes uncommitted if its active neighbors are in a tie, or all neighbors are the uncommitted. Numerical simulations were performed on square lattices of different linear size with periodic boundary conditions. Starting from a random distribution of active voters, the model leads to a stable non-consensus state in which three opinions coexist. We found that the "magnetization" of the non-consensus state and the concentration of uncommitted voters in it are governed by an initial composition of system and are independent of the lattice size. Furthermore, we found that a configuration of the stable non-consensus state undergoes a second order percolation transition at a critical concentration of voters holding the same opinion. Numerical simulations suggest that this transition belongs to the same universality class as the Ising percolation. These findings highlight the effect of an updating rule for a tie between voter neighbors on the critical behavior of models obeying the majority vote rule whenever a strict majority exists.

  7. Modeling Dark Energy Through AN Ising Fluid with Network Interactions

    NASA Astrophysics Data System (ADS)

    Luongo, Orlando; Tommasini, Damiano

    2014-12-01

    We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω0, becomes ω0 = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier-Polarsky-Linder (CPL) parametrization.

  8. Phase transitions in the three-state Ising spin-glass model with finite connectivity.

    PubMed

    Erichsen, R; Theumann, W K

    2011-06-01

    The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase transitions in the three-state Ghatak-Sherrington (or random Blume-Capel) model of a spin glass with a crystal-field term. The replica symmetry ansatz for the order function is expressed in terms of a two-dimensional effective-field distribution, which is determined numerically by means of a population dynamics procedure. Phase diagrams are obtained exhibiting phase boundaries that have a reentrance with both a continuous and a genuine first-order transition with a discontinuity in the entropy. This may be seen as "inverse freezing," which has been studied extensively lately, as a process either with or without exchange of latent heat.

  9. Universal Finite Size Corrections and the Central Charge in Non-solvable Ising Models

    NASA Astrophysics Data System (ADS)

    Giuliani, Alessandro; Mastropietro, Vieri

    2013-11-01

    We investigate a non-solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all and λ 0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.

  10. Probabilistic Cellular Automata for Low-Temperature 2-d Ising Model

    NASA Astrophysics Data System (ADS)

    Procacci, Aldo; Scoppola, Benedetto; Scoppola, Elisabetta

    2016-12-01

    We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the 2-d low-temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type contours.

  11. Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models

    NASA Astrophysics Data System (ADS)

    Si, Lisha; Liao, Xiaoyun; Zhou, Nengji

    2016-12-01

    With the developed "extended Monte Carlo" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L = 8912, significantly refining the results in earlier literature. In the strong-disorder regime, a new universality class of the Ising-type lattice model is unveiled with the exponents β = 0.304(5) , ν = 1.32(3) , z = 1.12(1) , and ζ = 0.90(1) , quite different from that of the quenched Edwards-Wilkinson equation.

  12. Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces

    NASA Astrophysics Data System (ADS)

    Cozzi, Matteo; Dipierro, Serena; Valdinoci, Enrico

    2017-06-01

    This paper contains three types of results: the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane,

  13. Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model

    NASA Astrophysics Data System (ADS)

    Schneider, Simon; Mueller, Marco; Janke, Wolfhard

    2017-07-01

    We investigate the behavior of the deviation of the estimator for the density of states (DOS) with respect to the exact solution in the course of Wang-Landau and Stochastic Approximation Monte Carlo (SAMC) simulations of the two-dimensional Ising model. We find that the deviation saturates in the Wang-Landau case. This can be cured by adjusting the refinement scheme. To this end, the 1 / t-modification of the Wang-Landau algorithm has been suggested. A similar choice of refinement scheme is employed in the SAMC algorithm. The convergence behavior of all three algorithms is examined. It turns out that the convergence of the SAMC algorithm is very sensitive to the onset of the refinement. Finally, the internal energy and specific heat of the Ising model are calculated from the SAMC DOS and compared to exact values.

  14. The appropriateness of ignorance in the inverse kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Dunn, Benjamin; Battistin, Claudia

    2017-03-01

    We develop efficient ways to consider and correct for the effects of hidden units for the paradigmatic case of the inverse kinetic Ising model with fully asymmetric couplings. We identify two sources of error in reconstructing the connectivity among the observed units while ignoring part of the network. One leads to a systematic bias in the inferred parameters, whereas the other involves correlations between the visible and hidden populations and has a magnitude that depends on the coupling strength. We estimate these two terms using a mean field approach and derive self-consistent equations for the couplings accounting for the systematic bias. Through application of these methods on simple networks of varying relative population size and connectivity strength, we assess how and under what conditions the hidden portion can influence inference and to what degree it can be crudely estimated. We find that for weak to moderately coupled systems, the effects of the hidden units is a simple rotation that can be easily corrected for. For strongly coupled systems, the non-systematic term becomes large and can no longer be safely ignored, further highlighting the importance of understanding the average strength of couplings for a given system of interest.

  15. Phase transitions and relaxation dynamics of Ising models exchanging particles

    NASA Astrophysics Data System (ADS)

    Goh, Segun; Fortin, Jean-Yves; Choi, M. Y.

    2017-01-01

    A variety of systems in nature and in society are open and subject to exchanging their constituents with other systems (e.g., environments). For instance, in biological systems, cells collect necessary energy and material by exchange of molecules or ions. Similarly, countries, cities or research institutes evolve as their constituents move in or out. To probe the corresponding particle exchange dynamics in such systems, we consider two Ising models exchanging particles and establish a master equation describing the equilibrium phases as well as the non-equilibrium dynamics of the system. It is found that an additional stable phase emerges as a consequence of the particle exchange process. Furthermore, we formulate the Ginzburg-Landau theory which allows to probe correlation effects. Accordingly, critical slowing down is manifested and the associated dynamic exponent is computed in the linear relaxation regime. In particular, this approach is relevant for investigating the grand canonical description of the system plus environment, with particle exchange and state transitions taken into account explicitly.

  16. Monte Carlo Studies of the Fcc Ising Model.

    NASA Astrophysics Data System (ADS)

    Polgreen, Thomas Lee

    Monte Carlo simulations are performed on the antiferromagnetic fcc Ising model which is relevant to the binary alloy CuAu. The model exhibits a first-order ordering transition as a function of temperature. The lattice free energy of the model is determined for all temperatures. By matching free energies of the ordered and disordered phases, the transition temperature is determined to be T(,t) = 1.736 J where J is the coupling constant of the model. The free energy as determined by series expansion and the Kikuchi cluster variation method is compared with the Monte Carlo results. These methods work well for the ordered phase, but not for the disordered phase. A determination of the pair correlation in the disordered phase along the {100} direction indicates a correlation length of (DBLTURN) 2.5a at the phase transition. The correlation length exhibits mean-field-like temperature dependence. The Cowley-Warren short range order parameters are determined as a function of temperature for the first twelve nearest-neighbor shells of this model. The Monte Carlo results are used to determine the free parameter in a mean-field-like class of theories described by Clapp and Moss. The ability of these theories to predict ratios between pair potentials is tested with these results. In addition, evidence of a region of heterophase fluctuations is presented in agreement with x-ray diffuse scattering measurements on Cu(,3)Au. The growth of order following a rapid quench from disorder is studied by means of a dynamic Monte Carlo simulation. The results compare favorably with the Landau theory proposed by Chan for temperatures near the first-order phase transition. For lower temperatures, the results are in agreement with the theories of Lifshitz and Allen and Chan. In the intermediate temperature range, our extension of Chan's theory is able to explain our simulation results and recent experimental results.

  17. Applicability of n-vicinity method for calculation of free energy of Ising model

    NASA Astrophysics Data System (ADS)

    Kryzhanovsky, Boris; Litinskii, Leonid

    2017-02-01

    Here we apply the n-vicinity method of approximate calculation of the partition function to an Ising Model with the nearest neighbor interaction on D-dimensional hypercube lattice. We solve the equation of state for an arbitrary dimension D and analyze the behavior of the free energy. As expected, for large dimensions (D ≥ 3) the system demonstrates a phase transition of the second kind. In this case, we obtain a simple analytical expression for the critical value of the inverse temperature. When 3 ≤ D ≤ 7 this expression is in a very good agreement with the results of computer simulations. In the case of small dimensions (D = 1 , 2), there is a noticeable discrepancy with the known exact results.

  18. RG flow from ϕ 4 theory to the 2D Ising model

    NASA Astrophysics Data System (ADS)

    Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.

    2017-08-01

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

  19. Depinning transition and thermal fluctuations in the random-field Ising model.

    PubMed

    Roters, L; Hucht, A; Lübeck, S; Nowak, U; Usadel, K D

    1999-11-01

    We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.

  20. 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.

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

    PubMed

    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.

  2. Dynamics of the transverse Ising model with next-nearest-neighbor interactions.

    PubMed

    Guimarães, P R C; Plascak, J A; de Alcantara Bonfim, O F; Florencio, J

    2015-10-01

    We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function.

  3. Form factor expansions in the 2D Ising model and Painlevé VI

    NASA Astrophysics Data System (ADS)

    Mangazeev, Vladimir V.; Guttmann, Anthony J.

    2010-10-01

    We derive a Toda-type recurrence relation, in both high- and low-temperature regimes, for the λ-extended diagonal correlation functions C(N,N;λ) of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlevé VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their λ-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case C(0,1;λ) where a connection to PVI theory is not known. Combined with the results for diagonal correlations these give all the initial conditions required for the λ-extended version of quadratic difference equations for the correlation functions discovered by McCoy, Perk and Wu. The results obtained here should provide a further potential algorithmic improvement in the λ-extended case, and facilitate other developments.

  4. 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.

  5. 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.

  6. Exact algorithm for sampling the two-dimensional Ising spin glass.

    PubMed

    Thomas, Creighton K; Middleton, A Alan

    2009-10-01

    A sampling algorithm is presented that generates spin-glass configurations of the two-dimensional Edwards-Anderson Ising spin glass at finite temperature with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson, Proceedings of the Eighth Symposium on Discrete Algorithms (SIAM, Philadelphia, 1997), p 258] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin-glass samples. This algorithm is recursive: it computes probabilities for spins along a "separator" that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination rather than Gaussian elimination for sampling dimer configurations. For n spins and given floating point precision, the algorithm has an asymptotic run-time of O(n(3/2)); it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to n=128(2), with fixed and periodic boundary conditions.

  7. ±J Ising model on homogeneous Archimedean lattices

    NASA Astrophysics Data System (ADS)

    Valdés, J. F.; Lebrecht, W.; Vogel, E. E.

    2012-04-01

    We tackle the problem of finding analytical expressions describing the ground state properties of homogeneous Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for square lattices, triangular lattices and honeycomb lattices. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.0,1.0]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples allow to validate previously described theoretical analysis. It is found that the second method presents slight advantages over the first one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice have to do with the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.5 for each one of the lattices also shines light on the general trends of the properties described here.

  8. 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.

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

    NASA Astrophysics Data System (ADS)

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

    2017-10-01

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

  10. Non-Ising-like two-dimensional superconductivity in a bulk single crystal

    NASA Astrophysics Data System (ADS)

    Zhang, Q. R.; Rhodes, D.; Zeng, B.; Johannes, M. D.; Balicas, L.

    2016-09-01

    Both Nb3PdxSe7 and Ta4Pd3Te16 crystallize in a monoclinic point group while exhibiting superconducting transition temperatures as high as Tc˜3.5 and ˜4.7 K, respectively. Disorder was claimed to lead to the extremely large upper critical fields (Hc 2) observed in related compounds. Despite the presence of disorder and heavier elements, Hc 2s in Ta4Pd3Te16 are found to be considerably smaller than those of Nb3PdxSe7 while displaying an anomalous, nonsaturating linear dependence on temperature T for fields along all three crystallographic axes. In contrast, crystals of the latter compound displaying the highest Tcs display Hc 2∝(1-T /Tc) 1 /2 , which in monolayers of transition metal dichalcogenides is claimed to be evidence for an Ising paired superconducting state resulting from strong spin-orbit coupling. This anomalous T dependence indicates that the superconducting state of Nb3PdxSe7 is quasi-two-dimensional in nature. This is further supported by a nearly divergent anisotropy in upper-critical fields, i.e., γ =Hc2 b/Hc2 a' , upon approaching Tc. Hence, in Nb3PdxSe7 the increase of Tc correlates with a marked reduction in electronic dimensionality as observed, for example, in intercalated FeSe. For the Nb compound, Density functional theory (DFT) calculations indicate that an increase in the external field produces an anisotropic orbital response, with especially strong polarization at the Pd sites when the field is perpendicular to their square planar environment. The field also produces an anisotropic spin moment at both Pd sites. Therefore, DFT suggests the field-induced pinning of the spin to the lattice as a possible mechanism for decoupling the superconducting planes.

  11. Ising model in clustered scale-free networks.

    PubMed

    Herrero, Carlos P

    2015-05-01

    The Ising model in clustered scale-free networks has been studied by Monte Carlo simulations. These networks are characterized by a degree distribution of the form P(k)∼k(-γ) for large k. Clustering is introduced in the networks by inserting triangles, i.e., triads of connected nodes. The transition from a ferromagnetic (FM) to a paramagnetic (PM) phase has been studied as a function of the exponent γ and the triangle density. For γ>3 our results are in line with earlier simulations, and a phase transition appears at a temperature T(c)(γ) in the thermodynamic limit (system size N→∞). For γ≤3, a FM-PM crossover appears at a size-dependent temperature T(co), so the system remains in a FM state at any finite temperature in the limit N→∞. Thus, for γ=3, T(co) scales as lnN, whereas for γ<3, we find T(co)∼JN(z), where the exponent z decreases for increasing γ. Adding motifs (triangles in our case) to the networks causes an increase in the transition (or crossover) temperature for exponent γ>3 (or ≤3). For γ>3, this increase is due to changes in the mean values 〈k〉 and 〈k(2)〉, i.e., the transition is controlled by the degree distribution (nearest-neighbor connectivities). For γ≤3, however, we find that clustered and unclustered networks with the same size and distribution P(k) have different crossover temperature, i.e., clustering favors FM correlations, thus increasing the temperature T(co). The effect of a degree cutoff k(cut) on the asymptotic behavior of T(co) is discussed.

  12. 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.

  13. Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

    By performing a high-statistics simulation of the D =4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

  14. Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions.

    PubMed

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

    2016-06-03

    By performing a high-statistics simulation of the D=4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

  15. Implementation of Minimal Representations in 2d Ising Model Calculations

    DTIC Science & Technology

    1992-05-01

    Re r’ u. 60:252-262.263-276. 1941. [Ons44] Lars Onsager . Crystal statistics I. A two-dimensional model with an order-disorder transition. Physical Re...ID lattices but the subject really came to life in 1944 when Onsager [Ons44] derived an exact closed form expression for the partition function (see

  16. The quantum Ising model: finite sums and hyperbolic functions.

    PubMed

    Damski, Bogdan

    2015-10-30

    We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.

  17. The quantum Ising model: finite sums and hyperbolic functions

    NASA Astrophysics Data System (ADS)

    Damski, Bogdan

    2015-10-01

    We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.

  18. 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.

  19. Critical endpoint behavior in an asymmetric Ising model: application of Wang-Landau sampling to calculate the density of states.

    PubMed

    Tsai, Shan-Ho; Wang, Fugao; Landau, D P

    2007-06-01

    Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.

  20. Critical endpoint behavior in an asymmetric Ising model: Application of Wang-Landau sampling to calculate the density of states

    NASA Astrophysics Data System (ADS)

    Tsai, Shan-Ho; Wang, Fugao; Landau, D. P.

    2007-06-01

    Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.

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

    PubMed

    Cardozo, David Lopes; Holdsworth, Peter C W

    2016-04-27

    The magnetization probability density in d  =  2 and 3 dimensional Ising models in slab geometry of volume [Formula: see text] 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 [Formula: see text]and boundary conditions are discussed. In the limiting case [Formula: see text] of a macroscopically large slab ([Formula: see text]) the distribution is found to scale as a Gaussian function for all tested system sizes and boundary conditions.

  2. Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model.

    PubMed

    del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H

    2012-09-14

    The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.

  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. Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

    NASA Astrophysics Data System (ADS)

    Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard

    2014-11-01

    The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of β∞=0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension σ=0.12037(18), using the statistics of suppressed configurations.

  5. The 1D Ising model and the topological phase of the Kitaev chain

    SciTech Connect

    Greiter, Martin Schnells, Vera Thomale, Ronny

    2014-12-15

    It has been noted that the Kitaev chain, a p-wave superconductor with nearest-neighbor pairing amplitude equal to the hopping term Δ=t, and chemical potential μ=0, can be mapped into a nearest neighbor Ising model via a Jordan–Wigner transformation. Starting from the explicit eigenstates of the open Kitaev chain in terms of the original fermion operators, we elaborate that despite this formal equivalence the models are physically inequivalent, and show how the topological phase in the Kitaev chain maps into conventional order in the Ising model.

  6. Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method.

    PubMed

    Shevchenko, Yuriy; Nefedev, Konstantin; Okabe, Yutaka

    2017-05-01

    We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.137203]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.

  7. Dual geometric worm algorithm for two-dimensional discrete classical lattice models.

    PubMed

    Hitchcock, Peter; Sørensen, Erik S; Alet, Fabien

    2004-01-01

    We present a dual geometrical worm algorithm for two-dimensional Ising models. The existence of such dual algorithms was first pointed out by Prokof'ev and Svistunov [Phys. Rev. Lett. 87, 160601 (2001)

  8. Ground states of the Ising model on an anisotropic triangular lattice: stripes and zigzags.

    PubMed

    Dublenych, Yu I

    2013-10-09

    A complete solution of the ground-state problem for the Ising model on an anisotropic triangular lattice with the nearest-neighbor interactions in a magnetic field is presented. It is shown that this problem can be reduced to the ground-state problem for an infinite chain with the interactions up to the second neighbors. In addition to the known ground-state structures (which correspond to full-dimensional regions in the parameter space of the model), new structures are found (at the boundaries of these regions), in particular, zigzagging stripes similar to those observed experimentally in colloidal monolayers. Though the number of parameters is relatively large (four), all the ground-state structures of the model are constructed and analyzed and therefore the paper can be considered as an example of a complete solution of a ground-state problem for classical spin or lattice-gas models. The paper can also help to verify the correctness of some results obtained previously by other authors and concerning the ground states of the model under consideration.

  9. Inferring structural connectivity using Ising couplings in models of neuronal networks.

    PubMed

    Kadirvelu, Balasundaram; Hayashi, Yoshikatsu; Nasuto, Slawomir J

    2017-08-15

    Functional connectivity metrics have been widely used to infer the underlying structural connectivity in neuronal networks. Maximum entropy based Ising models have been suggested to discount the effect of indirect interactions and give good results in inferring the true anatomical connections. However, no benchmarking is currently available to assess the performance of Ising couplings against other functional connectivity metrics in the microscopic scale of neuronal networks through a wide set of network conditions and network structures. In this paper, we study the performance of the Ising model couplings to infer the synaptic connectivity in in silico networks of neurons and compare its performance against partial and cross-correlations for different correlation levels, firing rates, network sizes, network densities, and topologies. Our results show that the relative performance amongst the three functional connectivity metrics depends primarily on the network correlation levels. Ising couplings detected the most structural links at very weak network correlation levels, and partial correlations outperformed Ising couplings and cross-correlations at strong correlation levels. The result was consistent across varying firing rates, network sizes, and topologies. The findings of this paper serve as a guide in choosing the right functional connectivity tool to reconstruct the structural connectivity.

  10. Time-dependent Monte Carlo simulations of critical and Lifshitz points of the axial-next-nearest-neighbor Ising model.

    PubMed

    da Silva, Roberto; Alves, Nelson; Drugowich de Felício, Jose Roberto

    2013-01-01

    In this work, we study the critical behavior of second-order points, specifically the Lifshitz point (LP) of a three-dimensional Ising model with axial competing interactions [the axial-next-nearest-neighbor Ising (ANNNI) model], using time-dependent Monte Carlo simulations. We use a recently developed technique that helps us localize the critical temperature corresponding to the best power law for magnetization decay over time: (m(0)=1)~t(-β/νz), which is expected of simulations starting from initially ordered states. We obtain original results for the dynamic critical exponent z, evaluated from the behavior of the ratio F(2)(t)=(m(0)=0)/(2)(m(0)=1)~t(3/z), along the critical line up to the LP. We explore all the critical exponents of the LP in detail, including the dynamic critical exponent θ that characterizes the initial slip of magnetization and the global persistence exponent θ(g) associated with the probability P(t) that magnetization keeps its signal up to time t. Our estimates for the dynamic critical exponents at the Lifshitz point are z=2.34(2) and θ(g)=0.336(4), values that are very different from those of the three-dimensional Ising model (the ANNNI model without the next-nearest-neighbor interactions at the z axis, i.e., J(2)=0), i.e., z≈2.07 and θ(g)≈0.38. We also present estimates for the static critical exponents β and ν, obtained from extended time-dependent scaling relations. Our results for static exponents are in good agreement with previous works.

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

    PubMed

    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.

  12. 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.

  13. 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.

  14. Phase diagram of the transverse Ising model in a random field

    NASA Astrophysics Data System (ADS)

    Milman, F. S.; Hauser, P. R.; Figueiredo, W.

    1991-06-01

    We determine the phase diagram of the transverse Ising model with a trimodal distribution (sum of three δ functions) for a longitudinal random field at T=0, using a mean-field approximation. The phase diagram includes tricritical points, ordered critical points, a fourth-order point, critical end points, and a double critical end point. Our T=0 phase diagram is completely equivalent to the one obtained by Kaufman, Klunzinger, and Khurana for the random-field Ising model. We show that the temperature and the magnitude of the transverse field play a similar role.

  15. Gauge model with Ising vacancies: Multicritical behavior of self-avoiding surfaces

    NASA Astrophysics Data System (ADS)

    Maritan, A.; Seno, F.; Stella, A. L.

    1991-08-01

    A openZ2 gauge model with n-component-vector degrees of freedom on a dodecahedral lattice is coupled to an Ising system on the dual lattice. The statistics of interacting self-avoiding surfaces (SAS) is obtained in the n-->0 limit. At the percolative critical point an exact identification of the SAS critical behavior with that of Ising cluster hulls holds. This condition corresponds to a multicritical point for SAS, in universality class different from that of branched polymers. The model allows application of standard statistical methods to SAS. A mean-field calculation gives a phase diagram remarkably consistent with the above results.

  16. Monte Carlo Simulations of Compressible Ising Models: Do We Understand Them?

    NASA Astrophysics Data System (ADS)

    Landau, D. P.; Dünweg, B.; Laradji, M.; Tavazza, F.; Adler, J.; Cannavaccioulo, L.; Zhu, X.

    Extensive Monte Carlo simulations have begun to shed light on our understanding of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg-Wilson hamiltonian for systems with elastic degrees of freedom resulted in the prediction that there should be four distinct cases that would have different behavior, depending upon symmetries and thermodynamic constraints. We shall provide an account of the results of careful Monte Carlo simulations for a simple compressible Ising model that can be suitably modified so as to replicate all four cases.

  17. Empirical relations between static and dynamic exponents for Ising model cluster algorithms

    NASA Astrophysics Data System (ADS)

    Coddington, Paul D.; Baillie, Clive F.

    1992-02-01

    We have measured the autocorrelations for the Swendsen-Wang and the Wolff cluster update algorithms for the Ising model in two, three, and four dimensions. The data for the Wolff algorithm suggest that the autocorrelations are linearly related to the specific heat, in which case the dynamic critical exponent is zint,EW=α/ν. For the Swendsen-Wang algorithm, scaling the autocorrelations by the average maximum cluster size gives either a constant or a logarithm, which implies that zint,ESW=β/ν for the Ising model.

  18. 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.

  19. Critical phenomena in the majority voter model on two-dimensional regular lattices.

    PubMed

    Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl

    2014-05-01

    In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.

  20. Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones

    NASA Astrophysics Data System (ADS)

    Rahmatullaev, M. M.; Rozikov, U. A.

    2017-09-01

    For the Ising model on Cayley trees we give a very wide class of new Gibbs measures. We show that these new measures are extreme under some conditions on the temperature. We give a review of all known Gibbs measures of the Ising model on trees and compare them with our new measures.

  1. Functional form of the Parisi overlap distribution for the three-dimensional Edwards-Anderson Ising spin glass.

    PubMed

    Berg, Bernd A; Billoire, Alain; Janke, Wolfhard

    2002-04-01

    Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated systems. For certain probability densities this predicts the characteristic large x falloff behavior f(x) approximately exp(-ae(x)), a>0. Using a multicanonical Monte Carlo technique, we have measured the Parisi overlap distribution P(q) for the three-dimensional Edward-Anderson Ising spin glass at and below the critical temperature We find that a probability distribution related to extreme-order statistics gives an excellent description of P(q) over about 80 orders of magnitude.

  2. Exact solutions to plaquette Ising models with free and periodic boundaries

    NASA Astrophysics Data System (ADS)

    Mueller, Marco; Johnston, Desmond A.; Janke, Wolfhard

    2017-01-01

    An anisotropic limit of the 3d plaquette Ising model, in which the plaquette couplings in one direction were set to zero, was solved for free boundary conditions by Suzuki (1972) [1], who later dubbed it the fuki-nuke, or "no-ceiling", model. Defining new spin variables as the product of nearest-neighbour spins transforms the Hamiltonian into that of a stack of (standard) 2d Ising models and reveals the planar nature of the magnetic order, which is also present in the fully isotropic 3d plaquette model. More recently, the solution of the fuki-nuke model was discussed for periodic boundary conditions, which require a different approach to defining the product spin transformation, by Castelnovo et al. (2010) [2]. We clarify the exact relation between partition functions with free and periodic boundary conditions expressed in terms of original and product spin variables for the 2d plaquette and 3d fuki-nuke models, noting that the differences are already present in the 1d Ising model. In addition, we solve the 2d plaquette Ising model with helical boundary conditions. The various exactly solved examples illustrate how correlations can be induced in finite systems as a consequence of the choice of boundary conditions.

  3. Special course for Masters and PhD students: phase transitions, Landau theory, 1D Ising model, the dimension of the space and Cosmology

    NASA Astrophysics Data System (ADS)

    Udodov, Vladimir; Katanov Khakas State Univ Team

    2014-03-01

    Symmetry breaking transitions. The phenomenological (L.D.Landau, USSR, 1937) way to describe phase transitions (PT's). Order parameter and loss of the symmetry. The second derivative of the free energy changes jump wise at the transition, i.e. we have a mathematical singularity and second order PT (TC>0). Extremes of free energy. A point of loss of stability of the symmetrical phase. The eigenfrequency of PT and soft mode behavior. The conditions of applicability of the Landau theory (A.Levanyuk, 1959, V.Ginzburg, 1960). 1D Ising model and exact solution by a transfer matrix method. Critical exponents in the L.Landau PT's theory and for 1D Ising model. Scaling hypothesis (1965) for 1D Ising model with zero critical temperature. The order of PT in 1D Ising model in the framework of the R.Baxter approach. The anthropic principle and the dimension of the space. Why do we have a three-dimensional space? Big bang, the cosmic vacuum, inflation and PT's. Higgs boson and symmetry breaking transitions. Author acknowledges the support of Katanov Khakas State University.

  4. A Manifold of Pure Gibbs States of the Ising Model on the Lobachevsky Plane

    NASA Astrophysics Data System (ADS)

    Gandolfo, Daniel; Ruiz, Jean; Shlosman, Senya

    2015-02-01

    In this paper we construct many `new' Gibbs states of the Ising model on the Lobachevsky plane, the millefeuilles. Unlike the usual states on the integer lattices, our foliated states have infinitely many interfaces. The interfaces are rigid and fill the Lobachevsky plane with positive density. We also construct analogous states on the Cayley trees.

  5. Energy fluctuations and the singularity of specific heat in a 3D Ising model

    NASA Astrophysics Data System (ADS)

    Kaupuzs, Jevgenijs

    2004-05-01

    We study the energy fluctuations in 3D Ising model near the phase transition point. Specific heat is a relevant quantity which is directly related to the mean squared amplitude of the energy fluctuations in the system. We have made extensive Monte Carlo simulations in 3D Ising model to clarify the character of the singularity of the specific heat Cv based on the finite-size scaling of its maximal values Cvmax depending on the linear size of the lattice L. An original iterative method has been used which automatically finds the pseudocritical temperature corresponding to the maximum of Cv. The simulations made up to L <= 128 with application of the Wolff's cluster algorithm allowed us to verify the possible power-like as well as logarithmic singularity of the specific heat predicted by different theoretical treatments. The most challenging and interesting result we have obtained is that the finite-size scaling of Cvmax in 3D Ising model is well described by a logarithmic rather than power-like ansatz, just like in 2D case. Another modification of our iterative method has been considered to estimate the critical coupling of 3D Ising model from the Binder cumulant data within L ɛ [96; 384]. Furthermore, the critical exponent β has been evaluated from the simulated magnetization data within the range of reduced temperatures t >= 0.000086 and system sizes L <= 410.

  6. Multiple Ising models coupled to 2-d gravity: a CSD analysis

    NASA Astrophysics Data System (ADS)

    Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo

    1994-04-01

    We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.

  7. Critical Dynamics Behavior of the Wolff Algorithm in the Site-Bond-Correlated Ising Model

    NASA Astrophysics Data System (ADS)

    Campos, P. R. A.; Onody, R. N.

    Here we apply the Wolff single-cluster algorithm to the site-bond-correlated Ising model and study its critical dynamical behavior. We have verified that the autocorrelation time diminishes in the presence of dilution and correlation, showing that the Wolff algorithm performs even better in such situations. The critical dynamical exponents are also estimated.

  8. Fluctuation-dissipation relation in an Ising model without detailed balance.

    PubMed

    Andrenacci, Natascia; Corberi, Federico; Lippiello, Eugenio

    2006-04-01

    We consider the modified Ising model introduced by de Oliveira, Mendes, and Santos [J. Phys. A 26, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions that generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the nonstationary phase-ordering kinetics, the parametric plot of the integrated response function chi(t,t(w)) vs the autocorrelation function is different from that of the kinetic Ising model. However, splitting chi(t,t(w)) into a stationary and an aging term chi(t,t(w)) = chi(st)(t-t(w)) + chi(ag)(t,t(w)), we find chi(ag)(t,t(w)) approximately t(w)(-a(chi)) f(t/t(w)), and a numerical value of a(chi) consistent with a(chi)= 1/4, as in the kinetic Ising model.

  9. 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.

  10. 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.

  11. Magnetization-driven random-field Ising model at T=0

    NASA Astrophysics Data System (ADS)

    Illa, Xavier; Rosinberg, Martin-Luc; Shukla, Prabodh; Vives, Eduard

    2006-12-01

    We study the hysteretic evolution of the random field Ising model at T=0 when the magnetization M is controlled externally and the magnetic field H becomes the output variable. The dynamics is a simple modification of the single-spin-flip dynamics used in the H -driven situation and consists in flipping successively the spins with the largest local field. This allows one to perform a detailed comparison between the microscopic trajectories followed by the system with the two protocols. Simulations are performed on random graphs with connectivity z=4 (Bethe lattice) and on the three-dimensional cubic lattice. The same internal energy U(M) is found with the two protocols when there is no macroscopic avalanche and it does not depend on whether the microscopic states are stable or not. On the Bethe lattice, the energy inside the macroscopic avalanche also coincides with the one that is computed analytically with the H -driven algorithm along the unstable branch of the hysteresis loop. The output field, defined here as ΔU/ΔM , exhibits very large fluctuations with the magnetization and is not self-averaging. The relation to the experimental situation is discussed.

  12. 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.

  13. Local and cluster critical dynamics of the 3d random-site Ising model

    NASA Astrophysics Data System (ADS)

    Ivaneyko, D.; Ilnytskyi, J.; Berche, B.; Holovatch, Yu.

    2006-10-01

    We present the results of Monte Carlo simulations for the critical dynamics of the three-dimensional site-diluted quenched Ising model. Three different dynamics are considered, these correspond to the local update Metropolis scheme as well as to the Swendsen-Wang and Wolff cluster algorithms. The lattice sizes of L=10-96 are analysed by a finite-size-scaling technique. The site dilution concentration p=0.85 was chosen to minimize the correction-to-scaling effects. We calculate numerical values of the dynamical critical exponents for the integrated and exponential autocorrelation times for energy and magnetization. As expected, cluster algorithms are characterized by lower values of dynamical critical exponent than the local one: also in the case of dilution critical slowing down is more pronounced for the Metropolis algorithm. However, the striking feature of our estimates is that they suggest that dilution leads to decrease of the dynamical critical exponent for the cluster algorithms. This phenomenon is quite opposite to the local dynamics, where dilution enhances critical slowing down.

  14. Microscopic approach to critical phenomena at interfaces: An application to complete wetting in the Ising model

    NASA Astrophysics Data System (ADS)

    Orlandi, A.; Parola, A.; Reatto, L.

    2004-11-01

    We study how the formalism of the hierarchical reference theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid-state theory which implements the basic ideas of the Wilson momentum-shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and nonclassical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the nonuniversal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.

  15. Entanglement scaling and spatial correlations of the transverse-field Ising model with perturbations

    NASA Astrophysics Data System (ADS)

    Cole, Richard; Pollmann, Frank; Betouras, Joseph J.

    2017-06-01

    We study numerically the entanglement entropy and spatial correlations of the one-dimensional transverse-field Ising model with three different perturbations. First, we focus on the out-of-equilibrium steady state with an energy current passing through the system. By employing a variety of matrix-product state based methods, we confirm the phase diagram and compute the entanglement entropy. Second, we consider a small perturbation that takes the system away from integrability and calculate the correlations, the central charge, and the entanglement entropy. Third, we consider periodically weakened bonds, exploring the phase diagram and entanglement properties first in the situation when the weak and strong bonds alternate (period two bonds) and then the general situation of a period of n bonds. In the latter case we find a critical weak bond that scales with the transverse field as Jc'/J =(h/J ) n , where J is the strength of the strong bond, J' is that of the weak bond, and h is the transverse field. We explicitly show that the energy current is not a conserved quantity in this case.

  16. 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.

  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.

    PubMed

    Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

    2016-10-10

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

  19. Magnetic properties, Lyapunov exponent and superstability of the spin-{1}/{2} Ising-Heisenberg model on a diamond chain

    NASA Astrophysics Data System (ADS)

    Ananikian, N.; Hovhannisyan, V.

    2013-05-01

    The exactly solvable spin-{1}/{2} Ising-Heisenberg model on a diamond chain has been considered. We have found the exact results for the magnetization using the recursion relation method. The existence of the magnetization plateau has been observed at one third of the saturation magnetization in the antiferromagnetic case. Some ground-state properties of the model are examined. At low temperatures, the system has two ferrimagnetic (FRI1 and FRI2) phases and one paramagnetic (PRM) phase. Lyapunov exponents for the various values of the exchange parameters and temperatures have been analyzed. It has also been shown that the maximal Lyapunov exponent exhibits plateau. Lyapunov exponents exhibit different behavior for two ferrimagnetic phases. We have found the existence of the supercritical point for the multi-dimensional rational mapping of the spin-{1}/{2} Ising-Heisenberg model on a diamond chain for the first time in the absence of the external magnetic field and T→0 in the antiferromagnetic case.

  20. Spin-one Ising model for ice VII-plastic ice phase transitions.

    PubMed

    Matsumoto, Masakazu; Himoto, Kazuhiro; Tanaka, Hideki

    2014-11-26

    We propose a spin model compatible with ice VII-plastic ice phase transitions and critical phenomena discovered recently by computer simulations. The Blume-Capel spin-1 Ising model is extended in order to describe the entropic stabilization effect in the plastic ice phase. The model shares the same set of tricritical exponents with simulation, indicating that they are of the same universality class.

  1. 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.

  2. 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.

  3. 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.

  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. Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model.

    PubMed

    Strecka, Jozef; Canová, Lucia; Minami, Kazuhiko

    2009-05-01

    The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.

  6. Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

    NASA Astrophysics Data System (ADS)

    Bonaccorsi, E.; Merlino, S.; Pasero, M.; Macedonio, G.

    Microsommite, ideal formula [Na4K2(SO4)] [Ca2Cl2][Si6Al6O24], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite-davyne group of minerals, presenting an ABAB... stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P63 to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161Å=√3adav, c=5.358Å=cdav Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order-disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters Tc 750°C and β 0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125kJmol-1. The continuous order-disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.

  7. Emerging Modified Transverse-Field Ising Model On A Hydrogenated Silicon Surface

    NASA Astrophysics Data System (ADS)

    Ritter, Burkhard; Beach, Kevin

    2014-03-01

    Advances in the precise placement of dangling bonds on a hydrogenated silicon surface open the prospect of manufacturing large scale quantum dot arrays. Small clusters of specifically arranged quantum dots comprise a system of bistable, interacting cells. Starting from an extended Hubbard model and using a set of controlled Hilbert space truncations, we show that such a system of quantum dot cells can be mapped to a modified transverse-field Ising model with long-ranged interactions. Each cell is described by a pseudo-spin. Because we control cell orientation and placement, we can construct a wide range of structures, with ferromagnetic and antiferromagnetic chains as simple examples. The Ising-like model is amenable to stochastic series expansion Monte Carlo, allowing the simulation and characterization of large systems. Work supported by Alberta Innovates Technology Futures.

  8. Ising Model Spin S = 1 ON Directed BARABÁSI-ALBERT Networks

    NASA Astrophysics Data System (ADS)

    Lima, F. W. S.

    On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model with spin S = 1/2 was seen not to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decayed exponentially with time. On these networks the Ising model spin S = 1 is now studied through Monte Carlo simulations. However, in this model, the order-disorder phase transition is well defined in this system. We have obtained a first-order phase transition for values of connectivity m = 2 and m = 7 of the directed Barabási-Albert network.

  9. Spin-1 Ising model: exact damage-spreading relations and numerical simulations.

    PubMed

    Anjos, A S; Mariz, A M; Nobre, F D; Araujo, I G

    2008-09-01

    The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin- 12 Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.

  10. Impurity effect on entanglement asymptotic state in one-dimensional Ising system coupled to a dissipative environment

    NASA Astrophysics Data System (ADS)

    Sadiek, G.

    2017-07-01

    We consider a finite one-dimensional Ising spin chain under the influence of a dissipative Lindblad environment obeying the Born-Markovian constrain in presence of an external magnetic field with open boundary conditions. We study the effect of a single impurity, located at the terminal or center of the chain, on the time evolution and asymptotic steady state of the bipartite entanglement in the chain starting from a maximally entangled initial state. We found that the impurity has a significant effect on the bipartite entanglement of its nearest spins and can be used to tune their steady state value but has almost no noticeable impact on the far ones. At finite temperature, the thermal excitations suppress the dynamics of the system and reduce the value of the steady state and may completely wipe it out as the temperature is increased, which eliminates the effect of the impurity in that case.

  11. Suzuki-Trotter decomposition and renormalization of a transverse-field Ising model in two dimensions

    NASA Astrophysics Data System (ADS)

    Dudziński, M.; Sznajd, J.

    1997-06-01

    The combined Suzuki-Trotter decomposition and Niemeijer-van Leuween real-space renormalization-group techniques are used to study the critical properties of a two-dimensional Ising system with a transverse field. The inverse critical temperature as a function of the external field and the temperature dependence of the transverse component of the magnetization are found. It is also shown that any real-space renormalization-group procedure based on the simple generalization of the Niemeijer-van Leeuwen majority rule for one of the components of the total-cell spin does not preserve the symmetry of the quantum spin space.

  12. Mean-field-like behavior of the generalized voter-model-class kinetic Ising model

    NASA Astrophysics Data System (ADS)

    Krause, Sebastian M.; Böttcher, Philipp; Bornholdt, Stefan

    2012-03-01

    We analyze a kinetic Ising model with suppressed bulk noise, which is a prominent representative of the generalized voter model phase transition. On the one hand, we discuss the model in the context of social systems and opinion formation in the presence of a tunable social temperature. On the other hand, we characterize the abrupt phase transition. The system shows nonequilibrium dynamics in the presence of absorbing states. We slightly change the system to get a stationary-state model variant exhibiting the same kind of phase transition. Using a Fokker-Planck description and comparing to mean-field calculations, we investigate the phase transition, finite-size effects, and the effect of the absorbing states resulting in a dynamic slowing down.

  13. Multicritical behavior in a random-field Ising model under a continuous-field probability distribution.

    PubMed

    Salmon, Octavio R; Crokidakis, Nuno; Nobre, Fernando D

    2009-02-04

    A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the presence of a triple Gaussian random magnetic field, which is defined as a superposition of three Gaussian distributions with the same width σ, centered at H = 0 and H = ± H(0), with probabilities p and (1-p)/2, respectively. Such a distribution is very general and recovers, as limiting cases, the trimodal, bimodal and Gaussian probability distributions. In particular, the special case of the random-field Ising model in the presence of a trimodal probability distribution (limit [Formula: see text]) is able to present a rather nontrivial multicritical behavior. It is argued that the triple Gaussian probability distribution is appropriate for a physical description of some diluted antiferromagnets in the presence of a uniform external field, for which the corresponding physical realization consists of an Ising ferromagnet under random fields whose distribution appears to be well represented in terms of a superposition of two parts, namely a trimodal and a continuous contribution. The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution, which is known to be stable for the present system. A rich variety of phase diagrams is presented, with one or two distinct ferromagnetic phases, continuous and first-order transition lines, tricritical, fourth-order, critical end points and many other interesting multicritical phenomena. Additionally, the present model carries the possibility of destroying such multicritical phenomena due to an increase in the randomness, i.e. increasing σ, which represents a very common feature in real systems.

  14. Finite-size corrections in the Ising model with special boundary conditions

    NASA Astrophysics Data System (ADS)

    Izmailian, N. Sh.

    2010-11-01

    The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz (BK) is analyzed. We derive exact finite-size corrections for the free energy F of the critical ferromagnetic Ising model on the M×N square lattice with Brascamp-Kunz boundary conditions [H.J. Brascamp, H. Kunz, J. Math. Phys. 15 (1974) 66]. We show that finite-size corrections strongly depend not only on the boundary conditions but also on the shape and pattern of the lattice. In the limit N→∞ we obtain the expansion of the free energy and the inverse correlation lengths for infinitely long strip with BK boundary conditions. Our results are consistent with the conformal field theory prediction for the mixed boundary conditions.

  15. Monte Carlo method for critical systems in infinite volume: The planar Ising model.

    PubMed

    Herdeiro, Victor; Doyon, Benjamin

    2016-10-01

    In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.

  16. Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth-Metal Tetraborides

    NASA Astrophysics Data System (ADS)

    Dublenych, Yu. I.

    2012-10-01

    A complete and exact solution of the ground-state problem for the Ising model on the Shastry-Sutherland lattice in an applied magnetic field is found. The magnetization plateau at one third of the saturation value is shown to be the only possible fractional plateau in this model. However, stripe magnetic structures with 1/2 and 1/n (n>3) magnetization, observed in the rare-earth-metal tetraborides RB4, occur at the boundaries of the three-dimensional regions of the ground-state phase diagram. These structures give rise to new magnetization plateaus if interactions of longer range are taken into account. For instance, an additional third-neighbor interaction is shown to produce a 1/2 plateau. The results obtained significantly refine the understanding of the magnetization process in RB4 compounds, especially in TmB4 and ErB4, which are strong Ising magnets.

  17. Condensation of Helium in Aerogel and Athermal Dynamics of the Random-Field Ising Model

    NASA Astrophysics Data System (ADS)

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

    2014-08-01

    High resolution measurements reveal that condensation isotherms of He4 in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

  18. Thermodynamic quantities and phase diagrams of spin-1 Blume-Capel bilayer Ising model

    NASA Astrophysics Data System (ADS)

    Kantar, Ersin; Ertaş, Mehmet

    2015-06-01

    An effective field theory with correlations has been used to study the critical behavior of the spin-1 Blume-Capel bilayer Ising model on a square lattice. The effects of the Hamiltonian parameters on thermodynamic quantities and phase diagrams are investigated in detail. We found that the system exhibits the first and the second order transitions as well as tricritical point. Furthermore, we have observed that the change of tricritical point values depends on interaction parameters.

  19. Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions

    NASA Astrophysics Data System (ADS)

    Janke, W.; Kenna, R.

    2002-02-01

    The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analyzed. Leading and subdominant scaling behavior of the Fisher zeros are determined exactly. The exact finite-size scaling, with corrections, of the specific heat is determined both at critical and effective critical (pseudocritical) points. The shift exponents associated with the scaling of these effective critical points are not the same as the inverse correlation length critical exponent. All corrections to scaling are analytic.

  20. Smeared quantum phase transition in the dissipative random quantum Ising model

    NASA Astrophysics Data System (ADS)

    Vojta, Thomas; Hoyos, José A.

    2010-01-01

    We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [J.A. Hoyos, T. Vojta, Phys. Rev. Lett. 100 (2008) 240601] of smeared quantum phase transitions.

  1. Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice

    NASA Astrophysics Data System (ADS)

    Zhang, G. M.; Yang, C. Z.

    1994-11-01

    Within the general cluster framework of Kandel, Ben-Av, and Domany, we develop a cluster algorithm for Monte Carlo simulations of the antiferromagnetic Ising model on a triangular lattice. The algorithm does not suffer from problems of metastability and is extremely efficient even at T=0, which allows us to extract the static exponent η=0.5 as well as the effective dynamical critical exponent of the algorithm z=0.64+/-0.02.

  2. Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity

    NASA Astrophysics Data System (ADS)

    Bowick, Mark; Falcioni, Marco; Harris, Geoffrey; Marinari, Enzo

    1994-02-01

    We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.

  3. 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. Copyright © 2015, American Association for the Advancement of Science.

  4. Reentrant and forward phase diagrams of the anisotropic three-dimensional Ising spin glass.

    PubMed

    Güven, Can; Berker, A Nihat; Hinczewski, Michael; Nishimori, Hidetoshi

    2008-06-01

    The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely, ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.

  5. Phase diagram of the two-dimensional +/-J Ising spin glass.

    PubMed

    Nobre, F D

    2001-10-01

    The +/-J Ising spin glass [probabilities p and (1-p) associated with ferromagnetic and antiferromagnetic couplings, respectively] is studied by applying a real-space renormalization-group technique on a hierarchical lattice that approaches the square lattice. Within such a procedure, there is no spin-glass phase and only two finite-temperature phases are found, namely, the paramagnetic and ferromagnetic ones. In spite of a reasonably small computational effort, an accurate paramagnetic-ferromagnetic boundary is presented: the estimate for the slope at p=1 is in very good agreement with the well-known exact result, whereas the coordinates of the Nishimori point are determined within a high precision. Below the Nishimori point, such a boundary is not strictly vertical-contrary to the usual belief-in such a way that a small reentrance is found at low temperatures.

  6. Shear viscosity at the Ising-nematic quantum critical point in two-dimensional metals

    NASA Astrophysics Data System (ADS)

    Eberlein, Andreas; Patel, Aavishkar A.; Sachdev, Subir

    2017-02-01

    In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio (kB/ℏ )η /s , where η is the shear viscosity and s is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension d =2 by an expansion below d =5 /2 . The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: η scales in the same manner as a chiral conductivity, and the ratio η /s diverges at low temperature (T ) as T-2 /z, where z is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.

  7. Algorithmic modeling of the irrelevant sound effect (ISE) by the hearing sensation fluctuation strength.

    PubMed

    Schlittmeier, Sabine J; Weissgerber, Tobias; Kerber, Stefan; Fastl, Hugo; Hellbrück, Jürgen

    2012-01-01

    Background sounds, such as narration, music with prominent staccato passages, and office noise impair verbal short-term memory even when these sounds are irrelevant. This irrelevant sound effect (ISE) is evoked by so-called changing-state sounds that are characterized by a distinct temporal structure with varying successive auditory-perceptive tokens. However, because of the absence of an appropriate psychoacoustically based instrumental measure, the disturbing impact of a given speech or nonspeech sound could not be predicted until now, but necessitated behavioral testing. Our database for parametric modeling of the ISE included approximately 40 background sounds (e.g., speech, music, tone sequences, office noise, traffic noise) and corresponding performance data that was collected from 70 behavioral measurements of verbal short-term memory. The hearing sensation fluctuation strength was chosen to model the ISE and describes the percept of fluctuations when listening to slowly modulated sounds (f(mod) < 20 Hz). On the basis of the fluctuation strength of background sounds, the algorithm estimated behavioral performance data in 63 of 70 cases within the interquartile ranges. In particular, all real-world sounds were modeled adequately, whereas the algorithm overestimated the (non-)disturbance impact of synthetic steady-state sounds that were constituted by a repeated vowel or tone. Implications of the algorithm's strengths and prediction errors are discussed.

  8. Monte Carlo renormalization: the triangular Ising model as a test case.

    PubMed

    Guo, Wenan; Blöte, Henk W J; Ren, Zhiming

    2005-04-01

    We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.

  9. Inclusion of an applied magnetic field of arbitrary strength in the Ising model

    NASA Astrophysics Data System (ADS)

    March, N. H.

    2014-06-01

    By making use of the early work of Kowalski (1972) [4] in this Journal, we expose the simplicity by which, for the Ising chain, the partition function Z1(βJ,βh), where h denotes the applied magnetic field strength, can be constructed from the zero-field limit Z1(βJ,0) plus the explicit factor cosh(βh). Secondly, we use mean-field theory for the Ising model in four dimensions to prove a similar functional relation; namely that the partition function Z4(βJ,βh) is again solely a functional of the zero field partition function Z4(βJ,0) and βh.

  10. Dissipative quantum Ising model in a cold-atom spin-boson mixture

    NASA Astrophysics Data System (ADS)

    Orth, Peter P.; Stanic, Ivan; Le Hur, Karyn

    2008-05-01

    Using cold bosonic atoms with two (hyperfine) ground states, we introduce a spin-boson mixture that allows one to implement the quantum Ising model in a tunable dissipative environment. The first specie lies in a deep optical lattice with tightly confining wells and forms a spin array; spin-up (spin-down) corresponds to occupation by one (no) atom at each site. The second specie forms a superfluid reservoir. Different species are coupled coherently via laser transitions and collisions. Whereas the laser coupling mimics a transverse field for the spins, the coupling to the reservoir sound modes induces a ferromagnetic (Ising) coupling as well as dissipation. This gives rise to an order-disorder quantum phase transition where the effect of dissipation can be studied in a controllable manner.

  11. Renyi Correlations and Phase Transitions in the Transverse-Field Ising model

    NASA Astrophysics Data System (ADS)

    Singh, Rajiv; Devakul, Trithep

    2015-03-01

    We calculate T = 0 spin-spin correlation functions with respect to a probability distribution given by an integer power (n) of the reduced density matrix ρcirc;A, when a transverse-field Ising model (TFIM) system is bipartitioned by a planar interface. Using series expansion methods these calculations are done in the thermodynamic limit for arbitrary positive integer n, with n = 1 giving us the bulk correlations. We study the TFIM system on isotropic and anisotropic simple-cubic lattices. We examine the evidence for whether the critical point of the transition deviates from the bulk critical point as a function of n and whether the critical behavior lies in the 2 D or 4 D Ising universality classes as would be expected from a surface transition at finite temperature and a T = 0 bulk transition, respectively. Work supported in part by NSF Grant Number DMR-1306048.

  12. Effective field study of ising model on a double perovskite structure

    NASA Astrophysics Data System (ADS)

    Ngantso, G. Dimitri; El Amraoui, Y.; Benyoussef, A.; El Kenz, A.

    2017-02-01

    By using the effective field theory (EFT), the mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model adapted to a double perovskite structure has been studied. The EFT calculations have been carried out from Ising Hamiltonian by taking into account first and second nearest-neighbors interactions and the crystal and external magnetic fields. Both first- and second-order phase transitions have been found in phase diagrams of interest. Depending on crystal-field values, the thermodynamic behavior of total magnetization indicated the compensation phenomenon existence. The hysteresis behaviors are studied by investigating the reduced magnetic field dependence of total magnetization and a series of hysteresis loops are shown for different reduced temperatures around the critical one.

  13. 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.

  14. 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…

  15. Frustration in Vicinity of Transition Point of Ising Spin Glasses

    NASA Astrophysics Data System (ADS)

    Miyazaki, Ryoji

    2013-09-01

    We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is close to the critical concentration at zero temperature when the output of a function about frustration is equal to unity. The function is the derivative of the average number of frustrated plaquettes with respect to the average number of antiferromagnetic bonds. This relation is conjectured in Ising spin glasses with binary couplings on two-dimensional lattices, hierarchical lattices, and three-body Ising spin glasses with binary couplings on two-dimensional lattices. In addition, the same argument in the Sherrington--Kirkpatrick model yields a point that is identical to the replica-symmetric solution of the transition point at zero temperature.

  16. Ising t-J model close to half filling: a Monte Carlo study.

    PubMed

    Maśka, M M; Mierzejewski, M; Ferraz, A; Kochetov, E A

    2009-01-28

    Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.

  17. Laterally driven interfaces in the three-dimensional Ising lattice gas.

    PubMed

    Smith, Thomas H R; Vasilyev, Oleg; Maciołek, Anna; Schmidt, Matthias

    2010-08-01

    We study the steady state of a phase-separated driven Ising lattice gas in three dimensions using computer simulations with Kawasaki dynamics. An external force field F(z) acts in the x direction parallel to the interface, creating a lateral order parameter current j^{x}(z) which varies with distance z from the interface. Above the roughening temperature, our data for "shearlike" linear variation of F(z) are in agreement with the picture wherein shear acts as effective confinement in this system, thus suppressing the interfacial capillary-wave fluctuations. We find sharper magnetization profiles and reduced interfacial width as compared to equilibrium. Pair correlations are more suppressed in the vorticity direction y than in the driving direction; the opposite holds for the structure factor. Lateral transport of capillary waves occurs for those forms of F(z) for which the current j^{x}(z) is an odd function of z , for example the shearlike drive, and a "steplike" driving field. For a V-shaped driving force no such motion occurs, but capillary waves are suppressed more strongly than for the shearlike drive. These findings are in agreement with our previous simulation studies in two dimensions. Near and below the (equilibrium) roughening temperature the effective-confinement picture ceases to work, but the lateral motion of the interface persists.

  18. 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.

  19. 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.

  20. On the hysteresis behaviors of the higher spin Ising model

    NASA Astrophysics Data System (ADS)

    Akıncı, Ümit

    2017-10-01

    Hysteresis characteristics of the general Spin-S (S > 1) Blume-Capel model have been studied within the effective field approximation. Particular emphasis has been paid on the large negative valued crystal field region and it has been demonstrated for this region that, Spin-S Blume-Capel model has 2 S windowed hysteresis loop in low temperatures. Some interesting results have been obtained such as nested characteristics of the hysteresis loops of successive spin-S Blume-Capel model. Effect of the rising crystal field and temperature on these hysteresis behaviors have been investigated in detail and physical mechanisms have been given.

  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. 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

  3. Dynamical Ising model simulations of nucleation and growth in copper-cobalt alloys

    SciTech Connect

    Cerezo, A.; Hyde, J.M.; Setna, R.P.; Smith, G.D.W.; Miller, M.K.

    1992-12-31

    A simple dynamical Ising model on a fixed lattice with a single bond energy parameter has been used to simulate the kinetics of diffusion during solid-state phase transformations in binary metallic alloys. Results of these simulations are compared with direct real-space measurements of the atomic distributions of elements in alloys, obtained with the position-sensitive atom probe. Despite the simplicity of the model, there is good quantitative agreement between the development of microstructure in the simulation and the nucleation and growth of cobalt-rich precipitates in copper-cobalt alloys.

  4. Disorder Identification in Hysteresis Data: Recognition Analysis of the Random-Bond-Random-Field Ising Model

    SciTech Connect

    Ovchinnikov, O. S.; Jesse, S.; Kalinin, S. V.; Bintacchit, P.; Trolier-McKinstry, S.

    2009-10-09

    An approach for the direct identification of disorder type and strength in physical systems based on recognition analysis of hysteresis loop shape is developed. A large number of theoretical examples uniformly distributed in the parameter space of the system is generated and is decorrelated using principal component analysis (PCA). The PCA components are used to train a feed-forward neural network using the model parameters as targets. The trained network is used to analyze hysteresis loops for the investigated system. The approach is demonstrated using a 2D random-bond-random-field Ising model, and polarization switching in polycrystalline ferroelectric capacitors.

  5. Finitized Conformal Spectra of the Ising Model on the Klein Bottle and Möbius Strip

    NASA Astrophysics Data System (ADS)

    Chui, C. H. Otto; Pearce, Paul A.

    2002-06-01

    We study the conformal spectra of the critical square lattice Ising model on the Klein bottle and Möbius strip using Yang-Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang-Baxter techniques and functional equations can be used to study the conformal spectra of more general exactly solvable lattice models in these topologies. The results rely on certain properties of the eigenvalues which are confirmed numerically.

  6. Nagel scaling, relaxation, and universality in the kinetic ising model on an alternating isotopic chain

    PubMed

    Goncalves; Lopez De Haro M; Taguena-Martinez; Stinchcombe

    2000-02-14

    The dynamic critical exponent and the frequency and wave-vector dependent susceptibility of the kinetic Ising model on an alternating isotopic chain with Glauber dynamics are examined. The analysis provides a connection between a microscopic model and the Nagel scaling curve originally proposed to describe dielectric susceptibility measurements of several glass-forming liquids. While support is given to the hypothesis relating the Nagel scaling to multiple relaxation processes, it is also found that the scaling function may exhibit plateau regions and does not hold for all temperatures.

  7. Infinite disorder and correlation fixed point in the Ising model with correlated disorder

    NASA Astrophysics Data System (ADS)

    Chatelain, Christophe

    2017-03-01

    Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations of the Ising model (q = 2), directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percolation fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations.

  8. Minimal duality breaking in the Kallen Lehman approach to 3D Ising model: A numerical test

    NASA Astrophysics Data System (ADS)

    Astorino, Marco; Canfora, Fabrizio; Martínez, Cristián; Parisi, Luca

    2008-06-01

    A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperatures. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the Monte Carlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte Carlo results by introducing a more general duality breaking is shortly discussed.

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

    NASA Astrophysics Data System (ADS)

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

    2006-03-01

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

  10. Ising models of strongly coupled biological networks with multivariate interactions

    NASA Astrophysics Data System (ADS)

    Merchan, Lina; Nemenman, Ilya

    2013-03-01

    Biological networks consist of a large number of variables that can be coupled by complex multivariate interactions. However, several neuroscience and cell biology experiments have reported that observed statistics of network states can be approximated surprisingly well by maximum entropy models that constrain correlations only within pairs of variables. We would like to verify if this reduction in complexity results from intricacies of biological organization, or if it is a more general attribute of these networks. We generate random networks with p-spin (p > 2) interactions, with N spins and M interaction terms. The probability distribution of the network states is then calculated and approximated with a maximum entropy model based on constraining pairwise spin correlations. Depending on the M/N ratio and the strength of the interaction terms, we observe a transition where the pairwise approximation is very good to a region where it fails. This resembles the sat-unsat transition in constraint satisfaction problems. We argue that the pairwise model works when the number of highly probable states is small. We argue that many biological systems must operate in a strongly constrained regime, and hence we expect the pairwise approximation to be accurate for a wide class of problems. This research has been partially supported by the James S McDonnell Foundation grant No.220020321.

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  12. The Ising model for changes in word ordering rules in natural languages

    NASA Astrophysics Data System (ADS)

    Itoh, Yoshiaki; Ueda, Sumie

    2004-11-01

    The order of ‘noun and adposition’ is an important parameter of word ordering rules in the world’s languages. The seven parameters, ‘adverb and verb’ and others, depend strongly on the ‘noun and adposition’. Japanese as well as Korean, Tamil and several other languages seem to have a stable structure of word ordering rules, while Thai and other languages, which have the opposite word ordering rules to Japanese, are also stable in structure. It seems therefore that each language in the world fluctuates between these two structures like the Ising model for finite lattice.

  13. Onsager and Kaufman's Calculation of the Spontaneous Magnetization of the Ising Model

    NASA Astrophysics Data System (ADS)

    Baxter, R. J.

    2011-11-01

    Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C.N. Yang published a derivation in Physical Review. In 1971 Onsager gave some clues to his and Kaufman's method, and there are copies of their correspondence in 1950 now available on the Web and elsewhere. Here we review how the calculation appears to have developed, and add a copy of a draft paper, almost certainly by Onsager and Kaufman, that obtains the result.

  14. 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})

  15. Magnetization of the Ising model on the Sierpinski pastry-shell

    NASA Astrophysics Data System (ADS)

    Chame, Anna; Branco, N. S.

    1992-02-01

    Using a real-space renormalization group approach, we calculate the approximate magnetization in the Ising model on the Sierpinski Pastry-shell. We consider, as an approximation, only two regions of the fractal: the internal surfaces, or walls (sites on the border of eliminated areas), with coupling constants JS, and the bulk (all other sites), with coupling constants Jv. We obtain the mean magnetization of the two regions as a function of temperature, for different values of α= JS/ JV and different geometric parameters b and l. Curves present a step-like behavior for some values of b and l, as well as different universality classes for the bulk transition.

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

    PubMed

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

    2009-06-01

    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.

  17. The transverse Ising model: a guide for combined modalities of hyperthermia and imaging

    NASA Astrophysics Data System (ADS)

    Singh, Vanchna; Banerjee, Varsha

    2013-09-01

    We provide a simple theoretical framework using the transverse Ising model to understand heat dissipation when magnetic fluid hyperthermia is performed in conjunction with magnetic resonance imaging. This combined modality is of immense utility in remedial procedures for cancer, but observations related to decreased heat dissipation have cast doubt on its applicability in a clinical laboratory. Through a first-principle analysis, we provide practical procedures for eliminating this problem by easy manipulation of laboratory parameters. Their usage has been largely empirical to date. Our calculations provide a firm grounding to the ad hoc methodologies and are a significant step towards placing the combined modality in the mainstream of cancer remedy.

  18. Constraining quantum critical dynamics: (2+1)D Ising model and beyond.

    PubMed

    Witczak-Krempa, William

    2015-05-01

    Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish nonperturbative constraints on the linear-response dynamics of conformal QC systems at finite temperature, in spatial dimensions above 1. Specifically, we analyze the large frequency or momentum asymptotics of observables, which we use to derive powerful sum rules and inequalities. The general results are applied to the O(N) Wilson-Fisher fixed point, describing the QC Ising model when N=1. We focus on the order parameter and scalar susceptibilities, and the dynamical shear viscosity. Connections to simulations, experiments, and gauge theories are made.

  19. 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

  20. An Ising-like model for monolayer-monolayer coupling in lipid bilayers

    NASA Astrophysics Data System (ADS)

    Sornbundit, Kan; Modchang, Charin; Nuttavut, Narin; Ngamsaad, Waipot; Triampo, Darapond; Triampo, Wannapong

    2013-07-01

    We have proposed the Ising bilayer model to study the domain growth dynamics in lipid bilayers. Interactions within and between layers are adopted from recent experimental and theoretical data. We investigate the effects of the mismatch area on the domain coarsening dynamics in both symmetric and asymmetric lipid bilayers. To explore domain coarsening, we used the Monte Carlo (MC) method with a standard Kawasaki dynamics to simulate the systems. The results show that domains on both layers grow following a power-law and that the domains grow slower when the mismatch areas are increased.

  1. Monte Carlos studies of critical and dynamic phenomena in mixed bond Ising model

    NASA Astrophysics Data System (ADS)

    Santos-Filho, J. B.; Moreno, N. O.; de Albuquerque, Douglas F.

    2010-11-01

    The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.

  2. Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions

    NASA Astrophysics Data System (ADS)

    Pinho, S. T. R.; Haddad, T. A. S.; Salinas, S. R.

    We write the exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuations.

  3. Scaling and universality in the aging kinetics of the two-dimensional clock model.

    PubMed

    Corberi, Federico; Lippiello, Eugenio; Zannetti, Marco

    2006-10-01

    We study numerically the aging dynamics of the two-dimensional p -state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of nondisordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function chi(t,s) approximately or = s(-a)chif(t/s), we find a(chi) consistent with the value a(chi)=0.28 found in the two-dimensional Ising model.

  4. Non equilibrium magnetocaloric properties of Ising model defined on regular lattices with arbitrary coordination number

    NASA Astrophysics Data System (ADS)

    Vatansever, Erol; Akinci, Ümit; Yüksel, Yusuf

    2017-08-01

    Using the effective field theory, we have studied the non equilibrium magnetocaloric properties of Ising systems defined in a wide variety of lattice structures with coordination numbers z = 3 , 4 , 6 , 8 and 12. Effects of coordination number, as well as the presence of oscillating magnetic field on several magnetic and magnetocaloric properties such as the critical temperature, isothermal entropy variation and refrigerant capacity have been investigated and discussed in detail. According to our results, the low dimensional structures would be potential candidates in magnetocaloric refrigeration applications. Moreover, without losing the favorable magnetocaloric properties, the working temperature of a magnetocaloric material can be easily tuned by applying oscillating magnetic fields with proper amplitude and frequency which may be feasible in room temperature cooling applications.

  5. Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain

    NASA Astrophysics Data System (ADS)

    Coester, K.; Malitz, W.; Fey, S.; Schmidt, K. P.

    2013-11-01

    We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidence for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e., except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows us to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.

  6. Algebraic and group structure for bipartite anisotropic Ising model on a non-local basis

    NASA Astrophysics Data System (ADS)

    Delgado, Francisco

    2015-01-01

    Entanglement is considered a basic physical resource for modern quantum applications as Quantum Information and Quantum Computation. Interactions based on specific physical systems able to generate and sustain entanglement are subject to deep research to get understanding and control on it. Atoms, ions or quantum dots are considered key pieces in quantum applications because they are elements in the development toward a scalable spin-based quantum computer through universal and basic quantum operations. Ising model is a type of interaction generating entanglement in quantum systems based on matter. In this work, a general bipartite anisotropic Ising model including an inhomogeneous magnetic field is analyzed in a non-local basis. This model summarizes several particular models presented in literature. When evolution is expressed in the Bell basis, it shows a regular block structure suggesting a SU(2) decomposition. Then, their algebraic properties are analyzed in terms of a set of physical parameters which define their group structure. In particular, finite products of pulses in this interaction are analyzed in terms of SU(4) covering. Thus, evolution denotes remarkable properties, in particular those related potentially with entanglement and control, which give a fruitful arena for further quantum developments and generalization.

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

    NASA Astrophysics Data System (ADS)

    Viswanathan, G. M.

    2017-06-01

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

  8. The random-bond Ising model in 2.01 and 3 dimensions

    NASA Astrophysics Data System (ADS)

    Komargodski, Zohar; Simmons-Duffin, David

    2017-04-01

    We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2  <  d  <  4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d  =  2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d  =  2. If one trusts these computations also in d  =  3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d  =  3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the O(2) model in d  =  3, where we predict a large logarithmic correction to the infrared scaling of disorder.

  9. Mixed Algorithms in the Ising Model on Directed BARABÁSI-ALBERT Networks

    NASA Astrophysics Data System (ADS)

    Lima, F. W. S.

    On directed Barabási-Albert networks with two and seven neighbours selected by each added site, the Ising model does not seem to show a spontaneous magnetisation. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law for Metropolis and Glauber algorithms, but for Wolff cluster flipping the magnetisation decays exponentially with time. On these networks the magnetisation behaviour of the Ising model, with Glauber, HeatBath, Metropolis, Wolf or Swendsen-Wang algorithm competing against Kawasaki dynamics, is studied by Monte Carlo simulations. We show that the model exhibits the phenomenon of self-organisation (= stationary equilibrium) defined in Ref. 8 when Kawasaki dynamics is not dominant in its competition with Glauber, HeatBath and Swendsen-Wang algorithms. Only for Wolff cluster flipping the magnetisation, this phenomenon occurs after an exponentially decay of magnetisation with time. The Metropolis results are independent of competition. We also study the same process of competition described above but with Kawasaki dynamics at the same temperature as the other algorithms. The obtained results are similar for Wolff cluster flipping, Metropolis and Swendsen-Wang algorithms but different for HeatBath.

  10. Deterministic Ising dynamics

    SciTech Connect

    Creutz, M.

    1986-03-01

    A deterministic cellular automation rule is presented which simulates the Ising model. On each cell in addition to an Ising spin is a space-time parity bit and a variable playing the role of a momentum conjugate to the spin. The procedure permits study of nonequilibrium phenomena, heat flow, mixing, and time correlations. The algorithm can make full use of multispin coding, thus permitting fast programs involving parallel processing on serial machines.

  11. Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model

    NASA Astrophysics Data System (ADS)

    Gao, Xun; Wang, Sheng-Tao; Duan, L.-M.

    2017-01-01

    We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being nonuniversal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.

  12. Evidence for columnar order in the fully frustrated transverse field Ising model on the square lattice.

    PubMed

    Wenzel, Sandro; Coletta, Tommaso; Korshunov, Sergey E; Mila, Frédéric

    2012-11-02

    Using extensive classical and quantum Monte Carlo simulations, we investigate the ground-state phase diagram of the fully frustrated transverse field Ising model on the square lattice. We show that pure columnar order develops in the low-field phase above a surprisingly large length scale, below which an effective U(1) symmetry is present. The same conclusion applies to the quantum dimer model with purely kinetic energy, to which the model reduces in the zero-field limit, as well as to the stacked classical version of the model. By contrast, the 2D classical version of the model is shown to develop plaquette order. Semiclassical arguments show that the transition from plaquette to columnar order is a consequence of quantum fluctuations.

  13. Quantum Supremacy for Simulating a Translation-Invariant Ising Spin Model.

    PubMed

    Gao, Xun; Wang, Sheng-Tao; Duan, L-M

    2017-01-27

    We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being nonuniversal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.

  14. Solution of the antiferromagnetic Ising model with multisite interaction on a zigzag ladder.

    PubMed

    Jurčišinová, E; Jurčišin, M

    2014-09-01

    We consider the antiferromagnetic spin-1/2 Ising model with multisite interaction in an external magnetic field on an infinite zigzag ladder. The model is solved exactly by using the transfer matrix method. Using the exact expression for the total magnetization per site, the magnetic properties of the model are investigated in detail. The model exhibits the formation of magnetization plateaus for low temperatures, and it is shown that their properties depend strongly on the strength of the multisite interaction. 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. The macroscopic degeneracy of the ground states is investigated and discussed.

  15. Automata and the susceptibility of the square lattice Ising model modulo powers of primes

    NASA Astrophysics Data System (ADS)

    Guttmann, A. J.; Maillard, J.-M.

    2015-11-01

    We study the full susceptibility of the Ising model modulo powers of primes. We find exact functional equations for the full susceptibility modulo these primes. Revisiting some lesser-known results on discrete finite automata, we show that these results can be seen as a consequence of the fact that, modulo 2 r , one cannot distinguish the full susceptibility from some simple diagonals of rational functions which reduce to algebraic functions modulo 2 r , and, consequently, satisfy exact functional equations modulo 2 r . We sketch a possible physical interpretation of these functional equations modulo 2 r as reductions of a master functional equation corresponding to infinite order symmetries such as the isogenies of elliptic curves. One relevant example is the Landen transformation which can be seen as an exact generator of the Ising model renormalization group. We underline the importance of studying a new class of functions corresponding to ratios of diagonals of rational functions: they reduce to algebraic functions modulo powers of primes and they may have solutions with natural boundaries. Dedicated to R J Baxter, for his 75th birthday.

  16. The square lattice Ising model on the rectangle I: finite systems

    NASA Astrophysics Data System (ADS)

    Hucht, Alfred

    2017-02-01

    The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size L× M and temperature. We start with the dimer method of Kasteleyn, McCoy and Wu, construct a highly symmetric block transfer matrix and derive a factorization of the involved determinant, effectively decomposing the free energy of the system into two parts, F(L,M)={{F}\\text{strip}}(L,M)+F\\text{strip}\\text{res}(L,M) , where the residual part F\\text{strip}\\text{res}(L,M) contains the nontrivial finite-L contributions for fixed M. It is given by the determinant of a M/2× M/2 matrix and can be mapped onto an effective spin model with M Ising spins and long-range interactions. While F\\text{strip}\\text{res}(L,M) becomes exponentially small for large L/M or off-critical temperatures, it leads to important finite-size effects such as the critical Casimir force near criticality. The relations to the Casimir potential and the Casimir force are discussed.

  17. Anomalous mean-field behavior of the fully connected Ising model.

    PubMed

    Colonna-Romano, Louis; Gould, Harvey; Klein, W

    2014-10-01

    Although the fully connected Ising model does not have a length scale, we show that the critical exponents for thermodynamic quantities such as the mean magnetization and the susceptibility can be obtained using finite size scaling with the scaling variable equal to N, the number of spins. Surprisingly, the mean value and the most probable value of the magnetization are found to scale differently with N at the critical temperature of the infinite system, and the magnetization probability distribution is not a Gaussian, even for large N. Similar results inconsistent with the usual understanding of mean-field theory are found at the spinodal. We relate these results to the breakdown of hyperscaling and show that hyperscaling can be restored by increasing N while holding the Ginzburg parameter rather than the temperature fixed, or by doing finite size scaling at the pseudocritical temperature where the susceptibility is a maximum for a given value of N. We conclude that finite size scaling for the fully connected Ising model yields different results depending on how the mean-field limit is approached.

  18. 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.

  19. 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

  20. 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

    2016-03-08

    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.

  1. Can Ising model and/or QKPZ equation properly describe reactive-wetting interface dynamics?

    NASA Astrophysics Data System (ADS)

    Efraim, Yael; Taitelbaum, Haim

    2009-09-01

    The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a small (˜ 150 μm) Hg droplet that spreads on a thin (˜ 4000 Å) Ag substrate. We calculated the kinetic roughening exponents (growth and roughness), as well as the persistence exponent of points on the advancing interface. In this paper we address the question whether there exists a well-defined model to describe the interface dynamics of this system, by performing two sets of numerical simulations. The first one is a simulation of an interface propagating according to the QKPZ equation, and the second one is a landscape of an Ising chain with ferromagnetic interactions in zero temperature. We show that none of these models gives a full description of the dynamics of the experimental reactivewetting system, but each one of them has certain common growth properties with it. We conjecture that this results from a microscopic behavior different from the macroscopic one. The microscopic mechanism, reflected by the persistence exponent, resembles the Ising behavior, while in the macroscopic scale, exemplified by the growth exponent, the dynamics looks more like the QKPZ dynamics.

  2. Finite-size scaling for the ising model on the Möbius strip and the klein bottle.

    PubMed

    Kaneda, K; Okabe, Y

    2001-03-05

    We study the finite-size scaling properties of the Ising model on the Möbius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function p(m) for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at T = T(c) for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.

  3. Finite-Size Scaling for the Ising Model on the Möbius Strip and the Klein Bottle

    NASA Astrophysics Data System (ADS)

    Kaneda, Kazuhisa; Okabe, Yutaka

    2001-03-01

    We study the finite-size scaling properties of the Ising model on the Möbius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function p\\(m\\) for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at T = Tc for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

    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.

  5. 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.

  6. 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

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

    PubMed

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

    2014-07-16

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

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

    PubMed

    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 (h_{n}) 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 h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-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 h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.

  9. The Role of Interfaces in the Propagation of Damage in the Confined Ising Model

    NASA Astrophysics Data System (ADS)

    Rubio Puzzo, M. Leticia; Albano, Ezequiel V.

    2003-04-01

    The propagation of damage in a confined magnetic Ising film, with short range competing magnetic fields (h) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well defined critical temperature Tw(h). In fact, the competing fields causes the occurrence of an interface between magnetic domains of different orientation. For T < Tw(h) (T > Tw(h)) such interface is bounded (unbounded) to the walls, while right at Tw(h) the interface is essentially located at the center of the film. It is found that the spatio-temporal spreading of the damage becomes considerably enhanced by the presence of the interface, which act as a "catalyst" of the damage causing an enhancement of the total damaged area. The critical points for damage spreading are evaluated by extrapolation to the thermodynamic limit using a finite-size scaling approach. Furthermore, the wetting transition effectively shifts the location of the damage spreading critical points, as compared with the well known critical temperature of the order-disorder transition characteristic of the Ising model. Such a critical points are found to be placed within the non-wet phase.

  10. Damage propagation at the interface's localization-delocalization transition of the confined Ising model

    NASA Astrophysics Data System (ADS)

    Rubio Puzzo, M. Leticia; Albano, Ezequiel V.

    2002-09-01

    The propagation of damage in a confined magnetic Ising film, with short-range competing magnetic fields (h) acting at opposite walls, is studied by means of Monte Carlo simulations. Due to the presence of the fields, the film undergoes a wetting transition at a well-defined critical temperature Tw(h). In fact, the competing fields cause the occurrence of an interface between magnetic domains of different orientations. For TTw(h)] such an interface is bound (unbound) to the walls, while right at Tw(h) the interface is essentially located at the center of the film. It is found that the spatiotemporal spreading of the damage becomes considerably enhanced by the presence of the interface, which acts as a ``catalyst'' of the damage causing an enhancement of the total damaged area. The critical points for damage spreading are evaluated by extrapolation to the thermodynamic limit using a finite-size scaling approach. Furthermore, the wetting transition effectively shifts the location of the damage spreading critical points, as compared with the well-known critical temperature of the order-disorder transition characteristic of the Ising model. Such critical points are found to be placed within the nonwet phase.

  11. 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.

  12. One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

    NASA Astrophysics Data System (ADS)

    Monthus, Cécile

    2014-06-01

    For the one-dimensional long-ranged Ising spin-glass with random couplings decaying with the distance $r$ as $J(r) \\sim r^{-\\sigma}$ and distributed with the L\\'evy symmetric stable distribution of index $1 <\\mu \\leq 2$ (including the usual Gaussian case $\\mu=2$), we consider the region $\\sigma>1/\\mu$ where the energy is extensive. We study two real space renormalization procedures at zero temperature, namely a simple box decimation that leads to explicit calculations, and a strong disorder decimation that can be studied numerically on large sizes. The droplet exponent governing the scaling of the renormalized couplings $J_L \\propto L^{\\theta_{\\mu}(\\sigma)}$ is found to be $\\theta_{\\mu}(\\sigma)=\\frac{2}{\\mu}-\\sigma$ whenever the long-ranged couplings are relevant $\\theta_{\\mu}(\\sigma)=\\frac{2}{\\mu}-\\sigma \\geq -1$. For the statistics of the ground state energy $E_L^{GS}$ over disordered samples, we obtain that the droplet exponent $\\theta_{\\mu}(\\sigma) $ governs the leading correction to extensivity of the averaged value $\\overline{E_L^{GS}} \\simeq L e_0 +L^{\\theta_{\\mu}(\\sigma)} e_1$. The characteristic scale of the fluctuations around this average is of order $L^{\\frac{1}{\\mu}}$, and the rescaled variable $u=(E_L^{GS}-\\overline{E_L^{GS}})/L^{\\frac{1}{\\mu}}$ is Gaussian distributed for $\\mu=2$, or displays the negative power-law tail in $1/(-u)^{1+\\mu}$ for $u \\to -\\infty$ in the L\\'evy case $1<\\mu<2$.

  13. Annealed Ising model with site dilution on self-similar structures

    NASA Astrophysics Data System (ADS)

    Silva, V. S. T.; Andrade, R. F. S.; Salinas, S. R.

    2014-11-01

    We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ →∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T . Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.

  14. Slow relaxation in a constrained Ising spin chain: toy model for granular compaction.

    PubMed

    Majumdar, Satya N; Dean, David S

    2002-11-01

    We present detailed analytical studies on the zero-temperature coarsening dynamics in an Ising spin chain in the presence of a dynamically induced field that favors locally the "-" phase compared to the "+" phase. We show that the presence of such a local kinetic bias drives the system into a late time state with average magnetization m equal to -1. However the magnetization relaxes into this final value extremely slowly in an inverse logarithmic fashion. We further map this spin model exactly onto a simple lattice model of granular compaction that includes the minimal microscopic moves needed for compaction. This toy model then predicts analytically an inverse logarithmic law for the growth of density of granular particles, as seen in recent experiments and thereby provides a mechanism for the inverse logarithmic relaxation. Our analysis utilizes an independent interval approximation for the particle and the hole clusters and is argued to be exact at late times (supported also by numerical simulations).

  15. Annealed Ising model with site dilution on self-similar structures.

    PubMed

    Silva, V S T; Andrade, R F S; Salinas, S R

    2014-11-01

    We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ→∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T. Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.

  16. Type-dependent stochastic Ising model describing the dynamics of a non-symmetric feedback module.

    PubMed

    Gonzalez-Navarrete, Manuel

    2016-10-01

    We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernández et. al [13], and are useful since take account to inherent variability of gene expression. We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler [7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator.

  17. Ising model for neural data: Model quality and approximate methods for extracting functional connectivity

    NASA Astrophysics Data System (ADS)

    Roudi, Yasser; Tyrcha, Joanna; Hertz, John

    2009-05-01

    We study pairwise Ising models for describing the statistics of multineuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods—inversion of the Thouless-Anderson-Palmer equations and an approximation proposed by Sessak and Monasson—are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin-glass theory for the normal phase. We also show that a globally correlated input to the neurons in the network leads to a small increase in the average coupling. However, the pair-to-pair variation in the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signaling the need to include higher-order correlations to describe the statistics of large networks.

  18. Hierarchy of correlations for the Ising model in the Majorana representation

    NASA Astrophysics Data System (ADS)

    Gómez-León, Álvaro

    2017-08-01

    We study the quantum Ising model in D dimensions with the equation-of-motion technique and the Majorana representation for spins. The decoupling scheme used for the Green's functions is based on the hierarchy of correlations in position space. To lowest order, this method reproduces the well-known mean field phase diagram and critical exponents. When correlations between spins are included, we show how the appearance of thermal fluctuations and magnons strongly affects the physical properties. In one dimension and for B =0 we demonstrate that, to first order in correlations, thermal fluctuations completely destroy the ordered phase. For nonvanishing transverse field we show that the model exhibits different behavior than its classical counterpart, especially near the quantum critical point. We discuss the connection with the Dyson's equation formalism and the explicit form of the self-energies.

  19. The bulk, surface and corner free energies of the square lattice Ising model

    NASA Astrophysics Data System (ADS)

    Baxter, R. J.

    2017-01-01

    We use Kaufman’s spinor method to calculate the bulk, surface and corner free energies {f}{{b}},{f}{{s}},{f}{{s}}\\prime ,{f}{{c}} of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For {f}{{b}},{f}{{s}},{f}{{s}}\\prime our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. We note that the corner free energy f c depends only on the elliptic modulus k that enters the working, and not on the argument v, which means that VJ’s conjecture applies for the full anisotropic model. The only aspect of this paper that is new is the actual derivation of f c, but by reporting all four free energies together we can see interesting structures linking them.

  20. Specific-heat exponent and modified hyperscaling in the 4D random-field Ising model

    NASA Astrophysics Data System (ADS)

    Fytas, N. G.; Martín-Mayor, V.; Picco, M.; Sourlas, N.

    2017-03-01

    We report a high-precision numerical estimation of the critical exponent α of the specific heat of the random-field Ising model in four dimensions. Our result α =0.12(1) indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of θ via the anomalous dimensions η and \\barη . Our analysis benefited from a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent z of the maximum-flow algorithm used is also provided.

  1. 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.

  2. The three-dimensional Ising spin glass in an external magnetic field: the role of the silent majority

    NASA Astrophysics Data System (ADS)

    Baity-Jesi, M.; Baños, R. A.; Cruz, A.; Fernandez, L. A.; Gil-Narvion, J. M.; Gordillo-Guerrero, A.; Iñiguez, D.; Maiorano, A.; Mantovani, F.; Marinari, E.; Martin-Mayor, V.; Monforte-Garcia, J.; Muñoz Sudupe, A.; Navarro, D.; Parisi, G.; Perez-Gaviro, S.; Pivanti, M.; Ricci-Tersenghi, F.; Ruiz-Lorenzo, J. J.; Schifano, S. F.; Seoane, B.; Tarancon, A.; Tripiccione, R.; Yllanes, D.

    2014-05-01

    We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. However, we encounter dramatic fluctuations in the behaviour of the model: averages over all the data only describe the behaviour of a small fraction of the data. Therefore, we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where some of the measurements behave as the average, while the majority show signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.

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

    SciTech Connect

    Coffey, Mark W.

    2008-04-15

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

  4. 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

    2012-04-25

    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.

  5. 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.

  6. Kosterlitz-Thouless phase transition of the axial next-nearest-neighbor Ising model in two dimensions

    NASA Astrophysics Data System (ADS)

    Shirakura, T.; Matsubara, F.; Suzuki, N.

    2014-10-01

    The spin structure of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) is a renewed problem because different Monte Carlo (MC) simulation methods predicted different spin orderings. The usual equilibrium simulation predicts the occurrence of a floating incommensurate (IC) Kosterlitz-Thouless (KT) type phase, which never emerges in non-equilibrium relaxation (NER) simulations. In this paper, we first examine previously published results of both methods, and then investigate a higher transition temperature Tc1 between the IC and paramagnetic phases. In the usual equilibrium simulation, we calculate the chain magnetization on larger lattices (up to 512×512 sites) and estimate Tc1≈1.16J with frustration ratio κ (≡-J2/J1)=0.6. We examine the nature of the phase transition in terms of the Binder ratio gL of spin overlap functions and the correlation-length ratio ξ /L. In the NER simulation, we observe the spin dynamics in equilibrium states by means of an autocorrelation function and also observe the chain magnetization relaxations from the ground and disordered states. These quantities exhibit an algebraic decay at T ≲1.17J. We conclude that the two-dimensional ANNNI model actually admits an IC phase transition of the KT type.

  7. Missing mass approximations for the partition function of stimulus driven Ising models.

    PubMed

    Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon

    2013-01-01

    Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and N pat the number of unique patterns in the data, contrasting with the O(L2 (N) ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.

  8. Missing mass approximations for the partition function of stimulus driven Ising models

    PubMed Central

    Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon

    2013-01-01

    Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and Npat the number of unique patterns in the data, contrasting with the O(L2N) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding. PMID:23898262

  9. Information flow in a kinetic Ising model peaks in the disordered phase.

    PubMed

    Barnett, Lionel; Lizier, Joseph T; Harré, Michael; Seth, Anil K; Bossomaier, Terry

    2013-10-25

    There is growing evidence that for a range of dynamical systems featuring complex interactions between large ensembles of interacting elements, mutual information peaks at order-disorder phase transitions. We conjecture that, by contrast, information flow in such systems will generally peak strictly on the disordered side of a phase transition. This conjecture is verified for a ferromagnetic 2D lattice Ising model with Glauber dynamics and a transfer entropy-based measure of systemwide information flow. Implications of the conjecture are considered, in particular, that for a complex dynamical system in the process of transitioning from disordered to ordered dynamics (a mechanism implicated, for example, in financial market crashes and the onset of some types of epileptic seizures); information dynamics may be able to predict an imminent transition.

  10. 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.

  11. First-order transition and tricritical behavior of the transverse crystal field spin-1 Ising model

    NASA Astrophysics Data System (ADS)

    Costabile, Emanuel; Viana, J. Roberto; de Sousa, J. Ricardo; de Arruda, Alberto S.

    2015-06-01

    The phase diagram of the spin-1 Ising model in the presence of a transverse crystal-field anisotropy (Dx) is studied within the framework of an effective-field theory with correlation. The effect of the coordination number (z) on the phase diagram in the T -Dx plane is investigated. We observe only second-order transitions for coordination number z < 7, while that for z ≥ 7 we have first- and second-order transitions, with the presence of two tricritical points. The lower tricritical temperature (Tt) decreases monotonically with the increasing value of z, and in the limit of z → ∞ we found Tt = 0, corresponding to the mean-field solution [Ricardo de Sousa and Branco, Phys. Rev. E 77 (2008) 012104] with a single tricritical point in the phase diagram.

  12. 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

  13. Scaling of geometric phase versus band structure in cluster-Ising models

    NASA Astrophysics Data System (ADS)

    Nie, Wei; Mei, Feng; Amico, Luigi; Kwek, Leong Chuan

    2017-08-01

    We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z =1 or z =2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.

  14. 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.

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

    PubMed Central

    Weber, Marc; Buceta, Javier

    2016-01-01

    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

  16. Magnetic behavior of a mixed Ising 3/2 and 5/2 spin model.

    PubMed

    De la Espriella, N; Buendía, G M

    2011-05-04

    We perform Monte Carlo simulations in order to study the magnetic properties of the mixed spin-S = ± 3/2, ± 1/2 and spin-σ = ± 5/2, ± 3/2, ± 1/2 Ising model. The spins are alternated on a square lattice such that S and σ are nearest neighbors. We found that when the Hamiltonian includes antiferromagnetic interactions between the S and σ spins, ferromagnetic interactions between the spins S, and a crystal field, the system presents compensation temperatures in a certain range of the parameters. The compensation temperatures are temperatures below the critical point where the total magnetization is zero, and they have important technological applications. We calculate the finite-temperature phase diagrams of the system. We found that the existence of compensation temperatures depends on the strength of the ferromagnetic interaction between the S spins.

  17. Magnetic behavior of a mixed Ising 3/2 and 5/2 spin model

    NASA Astrophysics Data System (ADS)

    De La Espriella, N.; Buendía, G. M.

    2011-05-01

    We perform Monte Carlo simulations in order to study the magnetic properties of the mixed spin-S = ± 3/2, ± 1/2 and spin-σ = ± 5/2, ± 3/2, ± 1/2 Ising model. The spins are alternated on a square lattice such that S and σ are nearest neighbors. We found that when the Hamiltonian includes antiferromagnetic interactions between the S and σ spins, ferromagnetic interactions between the spins S, and a crystal field, the system presents compensation temperatures in a certain range of the parameters. The compensation temperatures are temperatures below the critical point where the total magnetization is zero, and they have important technological applications. We calculate the finite-temperature phase diagrams of the system. We found that the existence of compensation temperatures depends on the strength of the ferromagnetic interaction between the S spins.

  18. 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.

  19. Rhythmic behavior in a two-population mean-field Ising model.

    PubMed

    Collet, Francesca; Formentin, Marco; Tovazzi, Daniele

    2016-10-01

    Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

  20. Magnetic Quantum Phase Transitions of a Kondo Lattice Model with Ising Anisotropy

    NASA Astrophysics Data System (ADS)

    Zhu, Jian-Xin; Kirchner, Stefan; Si, Qimiao; Grempel, Daniel R.; Bulla, Ralf

    2006-03-01

    We study the Kondo Lattice model with Ising anisotropy, within an extended dynamical mean field theory (EDMFT) in the presence or absence of antiferromagnetic ordering. The EDMFT equations are studied using both the Quantum Monte Carlo (QMC) and Numerical Renormalization Group (NRG) methods. We discuss the overall magnetic phase diagram by studying the evolution, as a function of the ratio of the RKKY interaction and bare Kondo scale, of the local spin susceptibility, magnetic order parameter, and the effective Curie constant of a nominally paramagnetic solution with a finite moment. We show that, within the numerical accuracy, the quantum magnetic transition is second order. The local quantum critical aspect of the transition is also discussed.

  1. A theory of solving TAP equations for Ising models with general invariant random matrices

    NASA Astrophysics Data System (ADS)

    Opper, Manfred; Çakmak, Burak; Winther, Ole

    2016-03-01

    We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeida-Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.

  2. Renormalization-group study of the ferromagnetic Ising model on the triangular lattice

    NASA Astrophysics Data System (ADS)

    Unger, Chris

    1984-08-01

    The dynamic real-space renormalization group of Mazenko and Valls is applied to the zero-field ferromagnetic Ising model on the triangular lattice. Renormalization equations valid for all temperatures above the critical temperature Tc are derived for the susceptibility, specific heat, structure factor, and correlation length. The magnetization is found for T

  3. Non-equilibrium steady states in two-temperature Ising models with Kawasaki dynamics

    NASA Astrophysics Data System (ADS)

    Borchers, Nick; Pleimling, Michel; Zia, R. K. P.

    2013-03-01

    From complex biological systems to a simple simmering pot, thermodynamic systems held out of equilibrium are exceedingly common in nature. Despite this, a general theory to describe these types of phenomena remains elusive. In this talk, we explore a simple modification of the venerable Ising model in hopes of shedding some light on these issues. In both one and two dimensions, systems attached to two distinct heat reservoirs exhibit many of the hallmarks of phase transition. When such systems settle into a non-equilibrium steady-state they exhibit numerous interesting phenomena, including an unexpected ``freezing by heating.'' There are striking and surprising similarities between the behavior of these systems in one and two dimensions, but also intriguing differences. These phenomena will be explored and possible approaches to understanding the behavior will be suggested. Supported by the US National Science Foundation through Grants DMR-0904999, DMR-1205309, and DMR-1244666

  4. Phase diagram of the random field Ising model on the Bethe lattice

    NASA Astrophysics Data System (ADS)

    Nowotny, Thomas; Patzlaff, Heiko; Behn, Ulrich

    2002-01-01

    The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regimes. Refining arguments of Bleher, Ruiz, and Zagrebnov [J. Stat. Phys. 93, 33 (1998)], an exact upper bound for the existence of a unique paramagnetic phase is found, which considerably improves the earlier results. Several numerical estimates of transition lines between a ferromagnetic and a paramagnetic regime are presented. The results obtained do not coincide with the lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If Bruinsma's estimate proves correct, this would hint at a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.

  5. Rhythmic behavior in a two-population mean-field Ising model

    NASA Astrophysics Data System (ADS)

    Collet, Francesca; Formentin, Marco; Tovazzi, Daniele

    2016-10-01

    Many real systems composed of a large number of interacting components, as, for instance, neural networks, may exhibit collective periodic behavior even though single components have no natural tendency to behave periodically. Macroscopic oscillations are indeed one of the most common self-organized behavior observed in living systems. In the present paper we study some dynamical features of a two-population generalization of the mean-field Ising model with the scope of investigating simple mechanisms capable to generate rhythms in large groups of interacting individuals. We show that the system may undergo a transition from a disordered phase, where the magnetization of each population fluctuates closely around zero, to a phase in which they both display a macroscopic regular rhythm. In particular, there exists a region in the parameter space where having two groups of spins with inter- and intrapopulation interactions of different strengths suffices for the emergence of a robust periodic behavior.

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

    NASA Astrophysics Data System (ADS)

    Schwerdtfeger, Christine A.; Mazziotti, David A.

    2009-06-01

    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

  7. 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

  8. Exact enumeration of an Ising model for Ni2MnGa

    NASA Astrophysics Data System (ADS)

    Eisenbach, Markus; Brown, Gregory; Nicholson, Don M.

    2014-03-01

    Exact evaluations of partition functions are generally prohibitively expensive due to exponential growth of phase space with the degrees of freedom. An Ising model with N sites has 2N possible states, requiring the use of better scaling methods, such as importance sampling Monte-Carlo for all but the smallest systems. Yet the ability to obtain exact solutions for large systems can provide important benchmark results and opportunities for unobscured insight into the underlying physics of the system. Here we present an Ising model for the magnetic sublattices of the important magneto-caloric material Ni2MnGa and use an exact enumeration algorithm to calculate the number of states g(E ,M1 ,M2) for each energy E and sublattice magnetization M1 and M2. This allows the efficient calculation of the partition function and derived thermodynamic quantities such as specific heat and susceptibility. Utilizing resources at the Oak Ridge Leadership Facility we are able to calculate g(E ,M1 ,M2) for systems of up to 48 sites, which provides important insight into the mechanism for the large magnet-caloric effect in Mn2NiGa as well as an important benchmark for Monte-Carlo based calculations (esp. Wang-Landau) of g(E ,M1 ,M2) . Work sponsored by the Division of Materials Science and Engineering, Office of Basic Energy Science, U.S. DOE. The research used resources of the Oak Ridge Leadership Computing Facility, supported by the Office of Science of DOE (DE-AC05-00OR22725).

  9. The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution

    NASA Astrophysics Data System (ADS)

    Lindgren, Kristian; Olbrich, Eckehard

    2017-08-01

    We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.

  10. The Approach Towards Equilibrium in a Reversible Ising Dynamics Model: An Information-Theoretic Analysis Based on an Exact Solution

    NASA Astrophysics Data System (ADS)

    Lindgren, Kristian; Olbrich, Eckehard

    2017-06-01

    We study the approach towards equilibrium in a dynamic Ising model, the Q2R cellular automaton, with microscopic reversibility and conserved energy for an infinite one-dimensional system. Starting from a low-entropy state with positive magnetisation, we investigate how the system approaches equilibrium characteristics given by statistical mechanics. We show that the magnetisation converges to zero exponentially. The reversibility of the dynamics implies that the entropy density of the microstates is conserved in the time evolution. Still, it appears as if equilibrium, with a higher entropy density is approached. In order to understand this process, we solve the dynamics by formally proving how the information-theoretic characteristics of the microstates develop over time. With this approach we can show that an estimate of the entropy density based on finite length statistics within microstates converges to the equilibrium entropy density. The process behind this apparent entropy increase is a dissipation of correlation information over increasing distances. It is shown that the average information-theoretic correlation length increases linearly in time, being equivalent to a corresponding increase in excess entropy.

  11. 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.

  12. Is the full susceptibility of the square-lattice Ising model a differentially algebraic function?

    NASA Astrophysics Data System (ADS)

    Guttmann, A. J.; Jensen, I.; Maillard, J.-M.; Pantone, J.

    2016-12-01

    We study the class of non-holonomic power series with integer coefficients that reduce, modulo primes, or powers of primes, to algebraic functions. In particular we try to determine whether the susceptibility of the square-lattice Ising model belongs to this class, and more broadly whether the susceptibility is a solution of a differentially algebraic equation. Initial results on Tutte's nonlinear ordinary differential equation (ODE) and other simple quadratic nonlinear ODEs suggest that a large set of differentially algebraic power series solutions with integer coefficients might reduce to algebraic functions modulo primes, or powers of primes. Since diagonals of rational functions are well-known to reduce, modulo primes, or powers of primes, to algebraic functions, a large subset of differentially algebraic power series with integer coefficients may be viewed as a natural ‘nonlinear’ generalisation of diagonals of rational functions. Here we give several examples of series with integer coefficients and non-zero radius of convergence that reduce to algebraic functions modulo (almost) every prime (or power of a prime). These examples satisfy differentially algebraic equations with the encoding polynomial occasionally possessing quite high degree (and thus difficult to identify even with long series). These examples shed important light on the very nature of such differentially algebraic series. Additionally, we have extended both the high- and low-temperature Ising square-lattice susceptibility series to 5043 coefficients. We find that even this long series is insufficient to determine whether it reduces to algebraic functions modulo 3, 5, etc. This negative result is in contrast to the comparatively easy confirmation that the corresponding series reduce to algebraic functions modulo powers of 2. Finally we show that even with 5043 terms we are unable to identify an underlying differentially algebraic equation for the susceptibility, ruling out a number of

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

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

  15. Chaotic Ising-like dynamics in traffic signals

    PubMed Central

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

    2013-01-01

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

  16. Highlighting the Structure-Function Relationship of the Brain with the Ising Model and Graph Theory

    PubMed Central

    Das, T. K.; Abeyasinghe, P. M.; Crone, J. S.; Sosnowski, A.; Laureys, S.; Owen, A. M.; Soddu, A.

    2014-01-01

    With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions. PMID:25276772

  17. Highlighting the structure-function relationship of the brain with the Ising model and graph theory.

    PubMed

    Das, T K; Abeyasinghe, P M; Crone, J S; Sosnowski, A; Laureys, S; Owen, A M; Soddu, A

    2014-01-01

    With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.

  18. 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.

  19. Effect of next-nearest neighbor interactions on the dynamic order parameter of the Kinetic Ising model in an oscillating field

    NASA Astrophysics Data System (ADS)

    Baez, William D.; Datta, Trinanjan

    We study the effects of next-nearest neighbor (NNN) interactions in the two-dimensional ferromagnetic kinetic Ising model exposed to an oscillating field. By tuning the interaction ratio (p =JNNN /JNN) of the NNN (JNNN) to the nearest-neighbor (NN) interaction (JNN) we find that the model undergoes a transition from a regime in which the dynamic order parameter Q is equal to zero to a phase in which Q is not equal to zero. From our studies we conclude that the model can exhibit an interaction induced transition from a deterministic to a stochastic state. Furthermore, we demonstrate that the systemsˆˆe2ˆˆ80ˆˆ99 metastable lifetime is sensitive not only to the lattice size, external field amplitude, and temperature (as found in earlier studies) but also to additional interactions present in the system.

  20. A mean-field renormalisation-group approach to Ising and q = 3-state Potts models with long-range interactions in one dimension

    NASA Astrophysics Data System (ADS)

    Soares, C. E. K.; de Sousa, J. Ricardo; Branco, N. S.

    2017-09-01

    We study the one-dimensional Potts model with long-range interactions decaying with distance r as r 1 + σ. An extended mean-field renormalisation-group procedure is applied, such that three finite-size linear lattices are compared, in order to evaluate critical temperatures and exponents for the q = 2 (Ising model) and q = 3 (such that the transition is a continuous one) cases. Good results are obtained, whenever comparison with exact results or with other procedures is possible. Moreover, we evaluate the surface field exponent for these models. We have been able to go to rather large lattices and then a suitable finite-size scaling procedure is employed to obtain the results in the thermodynamic limit.