Related papers: Generalized mean field approximation for parallel …
Recently Baumann et al. [arXiv:0709.3228v1] studied the phase-ordering kinetics of the two-dimensional Ising model with uniform spatially quenched disorder by Monte-Carlo simulations. They found that the two-time response and correlation…
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
Over the last decades, various "non-linear" MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a…
Spin correlation functions (up to the 3-site one) of disordered Ising model with the nearest neighbour interaction are calculated and investigated within a two-site cluster approximation for both quenched and annealed cases. The approach…
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the…
We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…
This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to…
The relationship between the mean-field approximations in various interacting models of statistical physics and measures of classical and quantum correlations is explored. We present a method that allows us to bound the total amount of…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
The entropic sampling dynamics based on the reversible information transfer to and from the environment is applied to the globally coupled Ising model in the presence of an oscillating magnetic field. When the driving frequency is low…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models…
The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…
Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study convergence of…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view…
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…
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…