Phase diagram of a stochastic cellular automaton with long-range interactions

TL;DR

This paper studies a stochastic cellular automaton with long-range interactions that decay with distance, analyzing its phase diagram through Monte Carlo and mean field methods, and connecting it to the Domany-Kinzel automaton.

Contribution

It introduces a new cellular automaton model with power law long-range interactions and compares its phase diagram using Monte Carlo and mean field approaches.

Findings

Phase diagram characterized for various interaction ranges

Model reduces to Domany-Kinzel automaton in certain limits

Comparison between Monte Carlo and mean field results

Abstract

We introduce a stochastic cellular automaton with power law spatial decaying long-range interactions. In some limit this model reduces to the Domany-Kinzel cellular automaton. Monte Carlo and mean field calculations of the phase diagram of the model for different ranges of interactions are compared.