An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

Abstract

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram's enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single paramenter of the model the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

Typeset in LaTeX2e, 14 pages, 6 figures, references given in full format; ver. 2 corresponds to the published version

References in corpus (10)

• Traffic and Related Self-Driven Many-Particle Systems
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Avalanche and spreading exponents in systems with absorbing states
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• Solution of the Density Classification Problem with Two Cellular Automata Rules
• Roughening Transition in a One-Dimensional Growth Process
• Nature of phase transitions in a probabilistic cellular automaton with two absorbing states
• Precise Critical Exponents for the Basic Contact Process
• Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density

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• Assortative clustering in a one-dimensional population with replication strategies
• Inefficiency of the block approximation in diploid Probabilistic Cellular Automata