Kinetic surface roughening for the Mullins-Herring equation

TL;DR

This paper derives analytical expressions for surface roughness and correlations in the Mullins-Herring equation, revealing scaling behaviors and critical exponents across dimensions, especially highlighting super roughness and Family-Vicsek scaling in one dimension.

Contribution

It provides an exact analytical solution for the Mullins-Herring equation's surface properties, enabling the determination of critical exponents and scaling behaviors in any dimension.

Findings

Analytic form for global mean-square surface width

Correlation functions derived for arbitrary dimensions

Identification of super roughness and Family-Vicsek scaling in 1D

Abstract

Using the linearity property of the Mullins-Herring equation when the velocity is zero with a Gaussian noise, we obtain an analytic form for the global mean-square surface width and height-height correlation function. This can be used to read the critical exponents in any dimension. In particular for d=1 we show that although the surface is super rough the system exhibits Family-Vicsek scaling behavior.