Order of the transition versus space dimension in a family of cellular automata

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Abstract
A mean-field theory of (probabilistic) cellular automata is developed and used to select a typical local rule whose mean-field analysis predicts first-order phase transitions. The corresponding automaton is then studied numerically on regular lattices for space dimensions d between 1 and 4. At odds with usual beliefs on two-state automata with one absorbing phase, first-order transitions are indeed exhibited as soon as d>1, with closer quantitative agreement with mean-field predictions for high space dimensions. For d=1, the transition is continuous, but with critical exponents different from those of directed percolation.