Lack of Self-affinity and Anomalous Roughening in Growth Processes

TL;DR

This paper challenges the common assumption of self-affinity in growth models, showing it is often absent except in specific cases, and proposes a new scaling approach for such non-self-affine surfaces.

Contribution

The authors demonstrate that self-affinity is not a universal property in growth models and introduce a new scaling framework for non-self-affine surfaces.

Findings

Self-affinity appears only at specific roughness exponents (1/2 or 1).

Most growth models lack self-affinity, contrary to common assumptions.

A new scaling picture better describes non-self-affine surface roughening.

Abstract

We contrast analytical results of a variety of growth models involving subdiffusion, thermal noise and quenched disorder with simulations of these models, concluding that the assumed self-affinity property is more an exception than a rule. In our two dimensional models, self-affine surfaces may only appear when the roughness exponent is $\chi = 1/2$ or $\chi = 1$. A new scaling picture, which leads to more suitable ways of determining the scaling exponents, is proposed when lack of self-affinity exists.