Phase Transitions of Cellular Automata

TL;DR

This paper investigates various phase transitions in cellular automata, applying statistical mechanics methods like Monte Carlo simulations, mean-field techniques, and renormalization group to understand complex behaviors.

Contribution

It introduces a comprehensive analysis of phase transitions in cellular automata, including new classifications and the application of advanced theoretical methods.

Findings

Identification of multiple types of phase transitions in cellular automata

Application of mean-field and renormalization group techniques to cellular automata

Insights into the effects of topology and rules on phase transition behavior

Abstract

We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic processes. We then formulate the cellular automaton problem using simple models, and illustrate different types of possible phase transitions: density phase transitions of first and second order, damage spreading, dilution of deterministic rules, asynchronism-induced transitions, synchronization phenomena, chaotic phase transitions and the influence of the topology. We illustrate the improved mean-field techniques and the phenomenological renormalization group approach.