General framework of the non-perturbative renormalization group for non-equilibrium steady states

TL;DR

This paper develops a comprehensive non-perturbative renormalization group framework for analyzing non-equilibrium steady states in stochastic systems, addressing technical challenges like causality and discretization.

Contribution

It introduces a detailed NPRG formalism for non-equilibrium steady states, including supersymmetric approaches and regularization techniques, with validation on Model A.

Findings

NPRG formalism effectively studies non-equilibrium steady states.

Supersymmetric NPRG simplifies causality handling.

Results for Model A are consistent across approaches.

Abstract

This paper is devoted to presenting in detail the non-perturbative renormalization group (NPRG) formalism to investigate out-of-equilibrium systems and critical dynamics in statistical physics. The general NPRG framework for studying non-equilibrium steady states in stochastic models is expounded and fundamental technicalities are stressed, mainly regarding the role of causality and of Ito's discretization. We analyze the consequences of Ito's prescription in the NPRG framework and eventually provide an adequate regularization to encode them automatically. Besides, we show how to build a supersymmetric NPRG formalism with emphasis on time-reversal symmetric problems, whose supersymmetric structure allows for a particularly simple implementation of NPRG in which causality issues are transparent. We illustrate the two approaches on the example of Model A within the derivative expansion approximation at order two, and check that they yield identical results.