Local structure approximation as a predictor of second order phase transitions in asynchronous cellular automata

TL;DR

This paper demonstrates that high-order local structure approximations can effectively predict second order phase transitions in $eta$-asynchronous cellular automata, specifically within the directed percolation universality class.

Contribution

It introduces a method using local structure approximation to forecast phase transitions in asynchronous cellular automata, advancing understanding of their critical behavior.

Findings

High-order local structure approximation predicts second order phase transitions.

Transitions belong to the directed percolation universality class.

Method provides a new tool for analyzing asynchronous cellular automata.

Abstract

We show that local structure approximation of sufficiently high order can predict the existence of second order phase transitions belonging to the directed percolation university class in $\alpha$-asynchronous cellular automata.