Exact solution of stochastic directed sandpile model
Statistical Mechanics
2009-10-31 v3
Abstract
We introduce and analytically solve a directed sandpile model with stochastic toppling rules. The model clearly belongs to a different universality class from its counterpart with deterministic toppling rules, previously solved by Dhar and Ramaswamy. The critical exponents are D_||=7/4, \tau=10/7 in two dimensions and D_||=3/2, \tau=4/3 in one dimension. The upper critical dimension of the model is three, at which the exponents apart from logarithmic corrections reach their mean-field values D_||=2, \tau=3/2.
Cite
@article{arxiv.cond-mat/0005528,
title = {Exact solution of stochastic directed sandpile model},
author = {Morten Kloster and Sergei Maslov and Chao Tang},
journal= {arXiv preprint arXiv:cond-mat/0005528},
year = {2009}
}
Comments
4 pages, 2 figures. Added numerical data for 3D case (2nd figure)