Sandpiles with height restrictions
Abstract
We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of particles per site), cannot exceed two. This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded. Two toppling rules are considered: in one, the particles are redistributed independently, while the other involves some cooperativity. We study the fixed-energy system (no input or loss of particles) using cluster approximations and extensive simulations, and find that it exhibits a continuous phase transition to an absorbing state at a critical value zeta_c of the particle density. The critical exponents agree with those of the unrestricted Manna sandpile.
Keywords
Cite
@article{arxiv.cond-mat/0203565,
title = {Sandpiles with height restrictions},
author = {Ronald Dickman and Tania Tome and Mario J. de Oliveira},
journal= {arXiv preprint arXiv:cond-mat/0203565},
year = {2009}
}
Comments
10 pages, 14 figures