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.

• Received 25 October 1988

DOI:https://doi.org/10.1103/PhysRevA.39.3094