Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation

TL;DR

This paper applies a nonperturbative renormalization group approach to study reaction-diffusion processes and directed percolation, successfully deriving critical exponents and microscopic reaction rates in various dimensions.

Contribution

It introduces a scale-dependent effective action framework that captures critical phenomena and computes reaction rates for phase transitions in reaction-diffusion systems.

Findings

Recovered critical exponents of directed percolation

Calculated microscopic reaction rates for phase transitions

Extended analysis to three-dimensional systems

Abstract

We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow equations, that are derived. They allow to recover the critical exponents of directed percolation, and moreover to calculate the microscopic reaction rates which give rise to a phase transition in the case of branching and annihilating random walks with odd number of offsprings, even in three dimensions.