Equilibrium and Non-equilibrium Ising Models by Means of PCA

We propose a unified approach to reversible and irreversible pca dynamics, and we show that in the case of 1D and 2D nearest neighbor Ising systems with periodic boundary conditions we are able to compute the stationary measure of the dynamics also when the latter is irreversible. We also show how,...

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Bibliographic Details
Published inJournal of statistical physics Vol. 153; no. 4; pp. 641 - 653
Main Authors Lancia, Carlo, Scoppola, Benedetto
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Probabilistic cellular automata
Markov chains
Equilibrium and non-equilibrium statistical mechanics
Stationary distribution
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Summary:We propose a unified approach to reversible and irreversible pca dynamics, and we show that in the case of 1D and 2D nearest neighbor Ising systems with periodic boundary conditions we are able to compute the stationary measure of the dynamics also when the latter is irreversible. We also show how, according to (P. Dai Pra et al. in J. Stat. Phys. 149(4):722–737, 2012 ), the stationary measure is very close to the Gibbs for a suitable choice of the parameters of the pca dynamics, both in the reversible and in the irreversible cases. We discuss some numerical aspects regarding this topic, including a possible parallel implementation.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-013-0847-0