Universality Class of Two-Offspring Branching Annihilating Random Walks

TL;DR

This paper investigates the critical behavior of a two-offspring branching annihilating random walk model, revealing it shares universality class characteristics with models having even offspring numbers and local parity conservation.

Contribution

The study demonstrates that the two-offspring BAW model belongs to the same universality class as higher-offspring models with parity conservation, supported by high-precision numerical critical exponents.

Findings

The transition belongs to the same universality class as models with even offspring n≥4.

Critical exponents are obtained with high accuracy.

The model's simplicity facilitates detailed numerical analysis.

Abstract

We analyze a two-offspring Branching Annihilating Random Walk ($n=2$ BAW) model, with finite annihilation rate. The finite annihilation rate allows for a dynamical phase transition between a vacuum, absorbing state and a non-empty, active steady state. We find numerically that this transition belongs to the same universality class as BAW's with an even number of offspring, $n\geq 4$, and that of other models whose dynamic rules conserve the parity of the particles locally. The simplicity of the model is exploited in computer simulations to obtain various critical exponents with a high level of accuracy.