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

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• 作者：Emilio N.M. Cirillo^a ; ^{emilio.cirillo@uniroma1.it" class="auth_mail} ; Pierre-Yves Louis^b ; ^{pierre-yves.louis@math.univ-poitiers.fr" class="auth_mail} ; Wioletta M. Ruszel^c ; ^{W.M.Ruszel@tudelft.nl" class="auth_mail} ; Cristian Spitoni^d ; ^{C.Spitoni@uu.nl" class="auth_mail}
• 刊名：Chaos, Solitons and Fractals
• 出版年：July 2014
• 年：2014
• 卷：64
• 期：Complete
• 页码：36-47
• 全文大小：676 K

文摘

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.