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Phase transitions of extended-range probabilistic cellular automata with two absorbing states

F. Bagnoli·F. Franci·R. Rechtman
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Abstract

We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by a competing ferromagnetic linear coupling and an antiferromagnetic nonlinear one. Despite its simplicity, this model exhibits an extremely rich phase diagram. We present numerical results and mean-field approximations.

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F. Bagnoli, F. Franci, R. Rechtman. 2004-10-01. Phase transitions of extended-range probabilistic cellular automata with two absorbing states. https://doi.org/10.1103/physreve.71.046108

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