Quantitative Phase Diagrams of Branching and Annihilating Random Walks

TL;DR

This paper uses nonperturbative renormalisation group methods to accurately compute phase diagrams for branching and annihilating random walks, confirming the existence of phase transitions across multiple dimensions and clarifying the role of mean field theory.

Contribution

It demonstrates the effectiveness of nonperturbative renormalisation group techniques in analyzing nonequilibrium phase transitions and provides new insights into the dimensional dependence of mean field behavior.

Findings

Absorbing phase transition exists in dimensions 1 to 6.

Mean field theory is only recovered as dimension approaches infinity.

Results are validated against detailed numerical simulations.

Abstract

We demonstrate the full power of nonperturbative renormalisation group methods for nonequilibrium situations by calculating the quantitative phase diagrams of simple branching and annihilating random walks and checking these results against careful numerical simulations. Specifically, we show, for the 2A->0, A -> 2A case, that an absorbing phase transition exists in dimensions d=1 to 6, and argue that mean field theory is restored not in d=3, as suggested by previous analyses, but only in the limit d -> $\infty$.