Roughness of Sandpile Surfaces

TL;DR

This paper investigates the surface roughness of sandpile models exhibiting self-organized criticality, revealing differences in roughness scaling definitions and clarifying the asymptotic behavior distinctions between critical and noncritical models.

Contribution

It demonstrates that different roughness definitions yield varying exponents in SOC models and clarifies the nature of crossovers in non-SOC models through analytical and numerical methods.

Findings

Different roughness definitions lead to distinct scaling exponents in SOC models.

No ambiguity in roughness scaling exists for non-SOC models.

Crossovers in non-SOC models can be mistaken for asymptotic behavior.

Abstract

We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields different asymptotic scaling exponents. Using approximate analytical arguments and extensive numerical studies we conclude that this ambiguity is due to the special scaling properties of the nonlinear steady state surface. We also find that there is no such ambiguity for non-SOC models, although there may be intermediate crossovers to different roughness values. Such crossovers need to be distinguished from the true asymptotic behaviour, as in the case of a noncritical disordered sandpile model studied in [10].