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

TL;DR

This paper studies a probabilistic cellular automaton combining rules 182 and 200, revealing a phase transition akin to directed percolation, with detailed analysis of its critical behavior and stationary states.

Contribution

It introduces a mean-field and Monte Carlo analysis of a mixed CA rule, identifying a phase transition in the directed percolation universality class.

Findings

Identifies a phase transition between extinction and survival states.

Characterizes the stationary density profile near the transition.

Observes slow, diffusive dynamics close to rule 200.

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.