Non perturbative renormalization group approach to surface growth

TL;DR

This paper introduces a real space renormalization group method for surface growth that effectively captures the KPZ fixed point properties, predicts no upper critical dimension, and aligns well with numerical results across various models.

Contribution

The paper presents a novel non-perturbative RG approach that accurately determines surface growth exponents and universality classes, surpassing limitations of traditional perturbative methods.

Findings

Successfully calculates roughness exponents up to 8 dimensions.

Predicts absence of an upper critical dimension for KPZ.

Reproduces observed phenomenology across different growth models.

Abstract

We present a recently introduced real space renormalization group (RG) approach to the study of surface growth. The method permits us to obtain the properties of the KPZ strong coupling fixed point, which is not accessible to standard perturbative field theory approaches. Using this method, and with the aid of small Monte Carlo calculations for systems of linear size 2 and 4, we calculate the roughness exponent in dimensions up to d=8. The results agree with the known numerical values with good accuracy. Furthermore, the method permits us to predict the absence of an upper critical dimension for KPZ contrarily to recent claims. The RG scheme is applied to other growth models in different universality classes and reproduces very well all the observed phenomenology and numerical results. Intended as a sort of finite size scaling method, the new scheme may simplify in some cases from a computational point of view the calculation of scaling exponents of growth processes.