Eur. Phys. J. B 72, 441-449 (2009)
https://doi.org/10.1140/epjb/e2009-00367-0

Diffusion in stochastic sandpiles

¹ Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Campus Universitário, National Institute of Science and Technology for Complex Systems, 59072-970, Natal, Rio Grande do Norte, Brazil
² Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, Minas Gerais, Brazil
³ National Institute of Science and Technology for Complex Systems, Caixa Postal 702, Belo Horizonte, Minas Gerais, Brazil

Corresponding author: ^a dickman@fisica.ufmg.br

Received: 8 June 2009
Revised: 17 August 2009
Published online: 31 October 2009

Abstract

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is possible, but with a narrow scaling region. We also develop a series expansion, in inverse powers of the density, for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with n particles is n(n-1), and compare the theoretical prediction with simulation results.