Roughness of Sandpile Surfaces

Details Roughness of Sandpile Surfaces Roughness of Sandpile Surfaces

2003-12-19

arxiv.org/abs/cond-mat/0312533v1

Phys. Rev. E 69, 031105 (2004)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 4 figures. Accepted for publication in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.69.031105

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].

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