Avalanche exponents and corrections to scaling for a stochastic sandpile

Details Avalanche exponents and corrections to scaling for a stochastic sandpile Avalanche exponents and corrections to scaling for a stochastic sandpile

2003-01-06

arxiv.org/abs/cond-mat/0301054v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures

Scientific paper

10.1103/PhysRevE.67.066111

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.

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