Critical Behavior of the Sandpile Model as a Self-Organized Branching Process

Abstract

Kinetic equations, which explicitly take into account the branching nature of sandpile avalanches, are derived. The dynamics of the sandpile model is described by the generating functions of a branching process. Having used the results obtained the renormalization group approach to the critical behavior of the sandpile model is generalized in order to calculate both critical exponents and height probabilities.