We numerically study avalanches in the two-dimensional Abelian sandpile model in terms of a sequence of waves of toppling events. Priezzhev et al. [Phys. Rev. Lett. 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 sk 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 ils 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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