Avalanche exponents and corrections to scaling for a stochastic sandpile

Ronald Dickman, J. M. M. Campelo

Published 2003-01-06Version 1

We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) avalanche distributions, in general, do not follow simple power laws, but rather have the form $P(s) \sim s^{-\tau_s} (\ln s)^{\gamma} f(s/s_c)$, with $f$ a cutoff function; (2) the exponents for sizes of dissipative avalanches in two dimensions differ markedly from the corresponding values for the Bak-Tang-Wiesenfeld (BTW) model, implying that the BTW and Manna models belong to distinct universality classes; (3) dissipative avalanche distributions obey finite size scaling, unlike in the BTW model.