Avalanches and waves in the Abelian sandpile model
نویسندگان
چکیده
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, Ds5sk2sk11 , where the size of the previous wave sk was considered to be almost always an upper bound for the size of the next wave sk11 . Here we show that the significant contribution to Ds comes from waves that violate the bound; the average ^Ds(sk)& is actually negative and diverges with the system size, contradicting the proposed solution. @S1063-651X~97!50510-1#
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