Reaction-diffusion processes and non-perturbative renormalisation group

TL;DR

This paper reviews recent advances in understanding non-equilibrium phase transitions in reaction-diffusion processes using non-perturbative renormalisation group methods, highlighting their importance for accurately capturing critical properties.

Contribution

It demonstrates the crucial role of non-perturbative techniques in analyzing the critical behavior of branching and annihilating random walks in reaction-diffusion systems.

Findings

Non-perturbative methods are essential for correct critical property analysis.

Critical properties depend strongly on non-perturbative features.

Review consolidates progress based on recent key studies.

Abstract

This paper is devoted to investigating non-equilibrium phase transitions to an absorbing state, which are generically encountered in reaction-diffusion processes. It is a review, based on [Phys. Rev. Lett. 92, 195703; Phys. Rev. Lett. 92, 255703; Phys. Rev. Lett. 95, 100601], of recent progress in this field that has been allowed by a non-perturbative renormalisation group approach. We mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non-perturbative features and that hence the use of a non-perturbative method turns out to be crucial to get a correct picture of the physics of these models.