Exact solution of a stochastic directed sandpile model.

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.