Branching annihilating random walks with parity conservation on a square lattice

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in two models of branching annihilating random walks with parity conservation on a square lattice, revealing distinct critical behaviors.

Contribution

It compares two variants of parity-conserving branching annihilating random walks, highlighting how different annihilation and creation rules affect critical behavior and universality.

Findings

Distinct critical behaviors observed in the two models

Annihilation and branching rules influence universality classes

Monte Carlo simulations reveal phase transition characteristics

Abstract

Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the first model the randomly walking particles annihilate when they meet and the branching process creates two additional particles; in the second case we distinguish particles and antiparticles created and annihilated in pairs. Quite distinct critical behavior is found in the two cases, raising the question of what determines universality in this kind of systems.