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 $D_{||}=7/4,$ $\tau =10/7\mathrm{}$ in two dimensions and $D_{||}=3/2,$ $\tau =4/3\mathrm{}$ 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 $D_{||}=2,$ $\tau =3/2.\mathrm{}$

• Received 5 June 2000

DOI:https://doi.org/10.1103/PhysRevE.63.026111