Cluster mean-field study of the parity conserving phase transition

TL;DR

This paper investigates the phase transition in a parity conserving process using N-cluster mean-field approximations, providing estimates for critical exponents and demonstrating the transition's persistence down to zero branching rate.

Contribution

It applies N-cluster mean-field approximations to analyze the parity conserving phase transition, extending understanding to zero branching rate and estimating critical exponents.

Findings

Phase transition observed for N <= 12.

Critical exponents estimated as ν⊥=1.85(3) and β=0.96(2).

Transition persists at zero branching rate.

Abstract

The phase transition of the even offspringed branching and annihilating random walk is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing to reach zero branching rate a phase transition can be seen for any N <= 12.The coherent anomaly extrapolations applied for the series of approximations results in $\nu_{\perp}=1.85(3)$ and $\beta=0.96(2)$.