Phase transitions of extended-range probabilistic cellular automata with two absorbing states

TL;DR

This paper investigates the complex phase transitions in a long-range one-dimensional cellular automaton with two absorbing states, revealing a rich phase diagram through numerical and mean-field analyses.

Contribution

It introduces a novel long-range cellular automaton model extending existing models like Ising and Domany-Kinzel, with detailed phase transition analysis.

Findings

Rich phase diagram with multiple transition types

Numerical and mean-field methods confirm phase behaviors

Model captures complex interactions in cellular automata

Abstract

We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by a competing ferromagnetic linear coupling and an antiferromagnetic nonlinear one. Despite its simplicity, this model exhibits an extremely rich phase diagram. We present numerical results and mean-field approximations.