Avalanches and Waves in the Abelian Sandpile Model

Details Avalanches and Waves in the Abelian Sandpile Model Avalanches and Waves in the Abelian Sandpile Model

1997-05-18

arxiv.org/abs/cond-mat/9705174v2

Physical Review E 56, Rapid Communications 3745 (1997)

Physics

Condensed Matter

Statistical Mechanics

RevTex, 4 pages, 4 postscript figures included (to appear in Phys. Rev. E Rapid Communications)

Scientific paper

10.1103/PhysRevE.56.R3745

We numerically study avalanches in the two dimensional Abelian sandpile model in terms of a sequence of waves of toppling events. Priezzhev et al [PRL 76, 2093 (1996)] have recently proposed exact results for the critical exponents in this model based on the existence of a proposed scaling relation for the difference in sizes of subsequent waves, $\Delta s =s_{k}- s_{k+1}$, where the size of the previous wave $s_{k}$ was considered to be almost always an upper bound for the size of the next wave $s_{k+1}$. Here we show that the significant contribution to $\Delta s$ comes from waves that violate the bound; the average $<\Delta s(s_{k})>$ is actually negative and diverges with the system size, contradicting the proposed solution.

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