Exact solution of stochastic directed sandpile model
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, 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.
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