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

TL;DR

This paper models sandpile avalanches as a self-organized branching process, deriving kinetic equations and using renormalization group techniques to analyze critical behavior, exponents, and probabilities.

Contribution

It introduces a novel kinetic equation framework for sandpile dynamics based on branching processes, extending the renormalization group approach for critical phenomena.

Findings

Derived kinetic equations for sandpile avalanches.

Calculated critical exponents and height probabilities.

Generalized renormalization group approach for self-organized criticality.

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.