The role of diffusion in branching and annihilation random walk models

TL;DR

This paper investigates diffusion effects in branching and annihilating random walk models using cluster mean-field methods and simulations, revealing phase diagram dependencies and transitions that challenge existing renormalization group predictions.

Contribution

It provides new insights into how diffusion influences phase diagrams and transitions in specific branching-annihilating models, with results confirmed by simulations.

Findings

Diffusion dependence in phase diagrams for A -> 2A, 2A -> 0 model.

Reentrant phase diagram in A -> 2A, 4A -> 0 model.

Directed percolation transitions observed at finite branching rates.

Abstract

Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by non-perturbative renormalization group method (L. Canet et al., cond-mat/0403423). The same type of survey for the A -> 2A, 4A -> 0 model results in a reentrant phase diagram, similar to that of 2A -> 3A, 4A -> 0 model (G. \'Odor, PRE {\bf 69}, 036112 (2004)). Simulations of the A -> 2A, 4A -> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.