The ideas behind self-consistent expansion

Abstract

In recent years we have witnessed a growing interest in various non-equilibriumsystems described in terms of stochastic nonlinear field theories. In some of thosesystems, like KPZ and related models, the interesting behavior is in the strongcoupling regime, which is inaccessible by traditional perturbative treatments such asdynamical renormalization group (DRG). A useful tool in the study of such systems isthe self-consistent expansion (SCE), which might be said to generate its own‘small parameter’. The self-consistent expansion (SCE) has the advantage that itsstructure is just that of a regular expansion, the only difference is that the simplesystem around which the expansion is performed is adjustable. The purpose of thispaper is to present the method in a simple and understandable way that hopefullywill make it accessible to a wider public working on non-equilibrium statisticalphysics.