Phase Transitions in a Nonequilibrium Percolation Model

TL;DR

This paper explores a nonequilibrium percolation model using cellular automata, revealing unique phase transitions, synchronized structures, and scaling violations, supported by simulations and analytical insights.

Contribution

It introduces a novel nonequilibrium percolation model exhibiting unique phase transition phenomena and scaling violations not seen in traditional percolation systems.

Findings

Identification of a critical region with phase transitions

Observation of synchronized stripe formations

Violation of finite-size scaling and hyperscaling relations

Abstract

We investigate the percolation properties of a two-state (occupied - empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a finite region of critical behavior, formation of synchronized stripes, additional phase transitions, as well as violation of the usual finite-size scaling and hyperscaling relations, phenomena that are very different from conventional percolation systems. We explain the mechanisms behind all these phenomena using computer simulations and analytic arguments.