Critical Properties of Stochastic Cellular Automata}

TL;DR

This paper investigates how combining different rules affects the behavior of one-dimensional stochastic cellular automata, revealing phase transitions and finite size effects through large-scale simulations.

Contribution

It provides the first large-scale numerical analysis of rule mixing effects on stochastic cellular automata, identifying new critical points and finite size effects.

Findings

Decay of magnetization studied in three phases

Finite size effects are significant near critical points

Large system sizes are necessary for accurate results

Abstract

We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its equilibrium value in the three phases. This requires system sizes in excess of 1 million sites. We also find severe finite size effects near the new critical points recently proposed on the basis of transfer matrix arguments.