Critical behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder

TL;DR

This study investigates how quenched spatial disorder affects the critical behavior of a parity conserving cellular automaton, revealing that weak disorder is irrelevant while strong disorder induces new transitions and variable critical exponents.

Contribution

It provides the first large-scale simulation analysis of disorder effects on a parity conserving cellular automaton, highlighting the impact of disorder strength on phase transitions.

Findings

Weak disorder does not alter universal critical behavior.

Strong disorder leads to exponential block size distribution and changing critical exponents.

A new transition within the inactive phase occurs due to diffusion walls under strong disorder.

Abstract

A stochastic cellular automaton exhibiting parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations. Numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model. This opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state. For very strong disorder the model breaks up to blocks with exponential size distribution and continuously changing critical exponents are observed. For strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model, in which residual particles survive the extinction. The critical dynamical behavior of this transition has been explored.