Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring

TL;DR

This paper investigates the critical behavior of branching annihilating random walks with four offspring, providing precise estimates of critical exponents and supporting a specific conjecture about their relationships.

Contribution

The study offers the first detailed numerical analysis of BAW with four offspring, confirming conjectured critical exponent ratios and expanding understanding of non-directed percolation universality classes.

Findings

Critical exponents estimated with high precision

Results support the conjecture: β/ν⊥=1/2, ν∥/ν⊥=7/4

Critical behavior differs from directed percolation

Abstract

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. {\bf 68}, 3060 (1992)], studied branching annihilating random walks (BAW) with $n=1$-5 offspring. These models exhibit a continuous phase transition to an absorbing state. For odd $n$ the models belong to the universality class of directed percolation. For even $n$ the particle number is conserved modulo 2 and the critical behavior is not compatible with directed percolation. In this article I study the BAW with $n=4$ using time-dependent simulations and finite-size scaling obtaining precise estimates for various critical exponents. The results are consistent with the conjecture: $\beta/\nuh = {1/2}$, $\nuv/\nuh = {7/4}$, $\gamma = 0$, $\delta = {2/7}$, $\eta = 0$, $z = {8/7}$, and $\delta_{h} = {9/2}$.