Branching rate expansion around annihilating random walks

TL;DR

This paper provides exact results for branching and annihilating random walks, including threshold values for phase transitions and insights into universality classes, using an expansion around pure annihilation.

Contribution

It introduces an expansion method around pure annihilation to analyze phase transitions in reaction-diffusion systems, with exact solutions in any dimension.

Findings

Computed the nonuniversal threshold for phase transition

Challenged existing scenarios for parity conserving class

Solved pure annihilation exactly in any dimension

Abstract

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.