Avalanche exponents and corrections to scaling for a stochastic sandpile

TL;DR

This paper investigates avalanche distributions in Manna's stochastic sandpile, revealing non-power-law behavior, differences from BTW model exponents, and finite size scaling for dissipative avalanches, indicating distinct universality classes.

Contribution

It demonstrates that avalanche distributions in the Manna model deviate from simple power laws and differ from BTW model exponents, establishing new universality class distinctions.

Findings

Avalanche distributions include logarithmic corrections to power laws.

Dissipative avalanche exponents differ from BTW model values.

Dissipative avalanches obey finite size scaling.

Abstract

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.