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Article Dans Une Revue Chaos, Solitons & Fractals Année : 2014

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

Résumé

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 \emph{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 \textit{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 (\textit{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.
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Dates et versions

hal-01283840 , version 1 (18-12-2023)

Identifiants

Citer

E. N. M. Cirillo, Pierre-Yves Louis, Wioletta M. Ruszel, C. Spitoni. Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata. Chaos, Solitons & Fractals, 2014, Nonequilibrium Statistical Mechanics: Fluctuations and Response, ⟨10.1016/j.chaos.2013.12.001⟩. ⟨hal-01283840⟩
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