Mean-field solution of the parity-conserving kinetic phase transition in one dimension

TL;DR

This paper develops a mean-field analytical approach to study the phase transition in a one-dimensional parity-conserving branching annihilating random walk model, successfully describing the transition and aligning with simulations.

Contribution

It introduces a modified parity interval method for finite reaction rates, providing one of the first analytical insights into the DP2 universality class.

Findings

Analytical description of the phase transition matches Monte Carlo results.

Exact analysis in the infinite reaction rate limit shows no active phase.

Finite reaction rates exhibit a transition well-captured by the modified method.

Abstract

A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class embracing systems that possess two symmetric absorbing states, which in one-dimensional systems, is in many cases equivalent to parity conservation. The phase transition is studied analytically through a mean-field like modification of the so-called {\it parity interval method}. The original method of parity intervals allows for an exact analysis of the diffusion-controlled limit of infinite reaction rate, where there is no active phase and hence no phase transition. For finite rates, we obtain a surprisingly good description of the transition which compares favorably with the outcome of Monte Carlo simulations. This provides one of the first analytical attempts to deal with the broadly studied DP2 universality class.