Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata

Emilio N.M. Cirillo, Pierre-Yves Louis, Wioletta M. Ruszel and Cristian Spitoni

Chaos, Solitons & Fractals, 2014, vol. 64, issue C, 36-47

Abstract: Cellular Automata are discrete-time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata (PCA), are discrete time Markov chains on lattice with finite single-cell states whose distinguishing feature is the parallel character of the updating rule. We study the ground states of the Hamiltonian and the low-temperature phase diagram of the related Gibbs measure naturally associated with a class of reversible PCA, called the cross PCA. In such a model the updating rule of a cell depends indeed only on the status of the five cells forming a cross centered at the original cell itself. In particular, it depends on the value of the center spin (self-interaction). The goal of the paper is that of investigating the role played by the self-interaction parameter in connection with the ground states of the Hamiltonian and the low-temperature phase diagram of the Gibbs measure associated with this particular PCA.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:64:y:2014:i:c:p:36-47

DOI: 10.1016/j.chaos.2013.12.001

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