Scaling Approach to Calculate Critical Exponents in Anomalous Surface Roughening

TL;DR

This paper introduces an analytical method to determine local surface fluctuation exponents in anomalous surface growth models, enabling prediction and calculation of when models exhibit anomalous scaling properties.

Contribution

The paper presents a novel analytical approach for calculating local scaling exponents in continuum growth models with anomalous surface roughening.

Findings

Method successfully predicts anomalous scaling conditions.

Applied to several continuum growth equations.

Provides explicit calculations of local exponents.

Abstract

We study surface growth models exhibiting anomalous scaling of the local surface fluctuations. An analytical approach to determine the local scaling exponents of continuum growth models is proposed. The method allows to predict when a particular growth model will have anomalous properties ($\alpha \neq \alpha_{loc}$) and to calculate the local exponents. Several continuum growth equations are examined as examples.