Phase transitions of cellular automata

Cellular automata (CA) are simple mathematical models of the dynamics of discrete variables in discrete space and time, with applications in nonequilibrium physics, chemical reactions, population dynamics and parallel computers. Phase transitions of stochastic CA with absorbing states are investigated. Using transfermatrix scaling the phase diagrams, critical properties and the entropy of one-dimensional CA are calculated. The corners of the phase diagrams reduce to deterministic CA discussed by Wolfram (Rev. Mod. Phys.55, 601 (1983)). Three-state models are introduced and, for special cases, exactly mapped onto two-state CA. The critical behaviour of other threestate models with one or two absorbing states and with immunization is investigated. Finally CA with competing reactions and/or with disorder are studied.

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