Scaling of Local Slopes, Conservation Laws and Anomalous Roughening in Surface Growth

TL;DR

This paper uses symmetry and conservation laws to analyze surface growth models, demonstrating that intrinsic anomalous roughening is unlikely in local models but super-roughening can occur under certain conserved dynamics.

Contribution

It provides a theoretical framework showing how symmetries and conservation laws restrict growth model behaviors, clarifying conditions for different roughening phenomena.

Findings

Intrinsic anomalous roughening cannot occur in local growth models.

Super-roughening may occur in some conserved dynamics.

Symmetries and conservation laws constrain the form of growth equations.

Abstract

We argue that symmetries and conservation laws greatly restrict the form of the terms entering the long wavelength description of growth models exhibiting anomalous roughening. This is exploited to show by dynamic renormalization group arguments that intrinsic anomalous roughening cannot occur in local growth models. However some conserved dynamics may display super-roughening if a given type of terms are present.