Journal of Statistical Physics

, Volume 153, Issue 4, pp 641–653 | Cite as

Equilibrium and Non-equilibrium Ising Models by Means of PCA

  • Carlo Lancia
  • Benedetto Scoppola


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.


Markov chains Probabilistic cellular automata Stationary distribution Equilibrium and non-equilibrium statistical mechanics 



The authors want to thank Elisabetta Scoppola and Paolo Dai Pra for the useful comments and discussions. The first author would like to express appreciation to Alexander Agathos and Salvatore Filippone for the useful comments regarding the cuda implementation; he would also like to address a very special thank to Thomas L. Falch and Johannes Kvam for their gargantuan help in developing and running the code.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Dept. of MathematicsUniversity of Rome Tor VergataRomeItaly

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