Avalanche exponents and corrections to scaling for a stochastic sandpile

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.

arXiv comment8 pages, 4 figures

References in corpus (6)

• Paths to Self-Organized Criticality
• The abelian sandpile and related models
• Absorbing-state phase transitions in fixed-energy sandpiles
• Universality in sandpiles
• On the scaling behavior of the abelian sandpile model
• Reaction-diffusion system with self-organized critical behavior

Cited by in corpus (8)

• Abelian Manna model on various lattices in one and two dimensions
• Steady state of Stochastic Sandpile Models
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Dissipative stochastic sandpile model on small world network : properties of non-dissipative and dissipative avalanches
• Absorbing phase transitions in a non-conserving sandpile model
• Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles
• Controlling Cost in Sandpile Models Through Local Adjustment of Drive
• Universality classes and crossover behaviors in non-Abelian directed sandpiles