Phys. Rev. E 63, 026111 (2001) [4 pages]Exact solution of a stochastic directed sandpile modelReceived 5 June 2000; published 24 January 2001 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, τ=10/7 in two dimensions and D||=3/2, τ=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, τ=3/2. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.63.026111
DOI:
10.1103/PhysRevE.63.026111
PACS:
05.65.+b, 05.40.-a, 05.70.Jk
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