Scale Invariant Dynamics of Surface Growth

TL;DR

This paper extends a nonperturbative renormalization group method to analyze surface growth, calculating critical exponents across dimensions and providing evidence against a finite upper critical dimension for KPZ growth.

Contribution

It introduces an improved RG approach for surface growth, accurately computes roughness exponents in various dimensions, and demonstrates the method's effectiveness on known linear models.

Findings

Calculated roughness exponent for KPZ in 1-9 dimensions

Provided evidence against finite upper critical dimension for KPZ

Successfully reproduced exact results for Edwards-Wilkinson model

Abstract

We describe in detail and extend a recently introduced nonperturbative renormalization group (RG) method for surface growth. The scale invariant dynamics which is the key ingredient of the calculation is obtained as the fixed point of a RG transformation relating the representation of the microscopic process at two different coarse-grained scales. We review the RG calculation for systems in the Kardar-Parisi-Zhang universality class and compute the roughness exponent for the strong coupling phase in dimensions from 1 to 9. Discussions of the approximations involved and possible improvements are also presented. Moreover, very strong evidence of the absence of a finite upper critical dimension for KPZ growth is presented. Finally, we apply the method to the linear Edwards-Wilkinson dynamics where we reproduce the known exact results, proving the ability of the method to capture qualitatively different behaviors.