Avalanches and Waves in the Abelian Sandpile Model

Abstract

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.

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

References in corpus (2)

• Universality in Sandpile Models
• Aging in a Model of Self-Organized Criticality

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• Expansion and Contraction of Avalanches in 2D Abelian Sandpile
• Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model
• Finite-size scaling of critical avalanches
• Fine Structure of Avalanches in the Abelian Sandpile Model
• Sandpile Model with Activity Inhibition
• Natural Measures on Polyominoes Induced by the Abelian Sandpile Model