相关论文: Generalization of the Mean-Field Ising Model Withi…

In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov…

The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…

A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very…

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…

The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…

We apply the Broad Histogram Method to an Ising system in the context of the recently reformulated Generalized Thermostatistics, and we claim it to be a very efficient simulation tool for this non-extensive statistics. Results are obtained…

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…

A mean-density description of spatially-inhomogeneous Bose-condensed gases based on Bogoliubov's method is introduced. The description assumes only a large mean atomic density and so remains valid when the mean field collapses due to phase…

We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…

A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…

The equipartition theorem states that inverse temperature equals the log-derivative of the density of states. This relation can be generalized by introducing a proportionality factor involving an increasing positive function phi(x). It is…

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…

We introduce a generalized thermostatistics based on Kolmogorov-Nagumo averages and appropriately selected information measures. The formalism includes Tsallis non-extensive thermostatistics, but also extensive thermostatistics based on…

A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff's mean-field approach with the model presented by one…

In this study, our effort is to introduce Tsallis thermostatistics in some details and to give a brief review of the magnetic systems which have been studied in the frame of this formalism.

The hyperensembles, introduced by Crooks in a context of non-equilibrium statistical physics, are considered here as a tool for systems in equilibrium. Simple examples like the ideal gas, the mean-field model, and the Ising interaction on…

Aim of this work is not trying to explore a macroscopic behavior of some recent model in statistical mechanics but showing how some recent techniques developed within the framework of spin glasses do work on simpler model, focusing on the…

The use of Mean-Field theory to unwrap principal phase patterns has been recently proposed. In this paper we generalize the Mean-Field approach to process phase patterns with arbitrary degree of undersampling. The phase unwrapping problem…