Avalanches and Waves in the Abelian Sandpile Model

الأصل · EN

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, Δs =sₖ- sₖ₊₁, where the size of the previous wave sₖ was considered to be almost always an upper bound for the size of the next wave sₖ₊₁. Here we show that the significant contribution to Δs comes from waves that violate the bound; the average <Δs(sₖ)> is actually negative and diverges with the system size, contradicting the proposed solution.