Non-perturbative renormalization of the KPZ growth dynamics

TL;DR

This paper presents a non-perturbative renormalization method for KPZ surface growth, accurately computing roughness exponents across multiple dimensions without an upper critical dimension, and overcoming previous methodological limitations.

Contribution

It introduces an indirect functional renormalization approach that identifies stable fixed points for KPZ dynamics in any dimension, improving upon traditional real space methods.

Findings

Roughness exponent $$ computed for dimensions 1 to 8.

Results agree well with existing simulations.

No evidence found for an upper critical dimension.

Abstract

We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic (self-affine) scaling are overcome with an indirect functional renormalization. The roughness exponent $\alpha$ is computed for dimensions $d=1$ to 8 and it results to be in very good agreement with the available simulations. No evidence is found for an upper critical dimension. We discuss how the present approach can be extended to other self-affine problems.