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

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

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.

Suggested Citation

  • Cirillo, Emilio N.M. & Louis, Pierre-Yves & Ruszel, Wioletta M. & Spitoni, Cristian, 2014. "Effect of self-interaction on the phase diagram of a Gibbs-like measure derived by a reversible Probabilistic Cellular Automata," Chaos, Solitons & Fractals, Elsevier, vol. 64(C), pages 36-47.
  • Handle: RePEc:eee:chsofr:v:64:y:2014:i:c:p:36-47
    DOI: 10.1016/j.chaos.2013.12.001
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    References listed on IDEAS

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    1. Perc, Matjaž & Grigolini, Paolo, 2013. "Collective behavior and evolutionary games – An introduction," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 1-5.
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