Dynamically Driven Renormalization Group Applied to Sandpile Models

TL;DR

This paper develops a new dynamically driven renormalization group framework to analyze the critical behavior of sandpile models, incorporating feedback from stationarity conditions to better understand avalanche dynamics.

Contribution

It introduces a novel renormalization approach that accounts for nonequilibrium dynamics and feedback, advancing the theoretical understanding of self-organized criticality in sandpile models.

Findings

Describes boundary and bulk critical behavior of sandpile models.

Provides a detailed branching process analysis of avalanches.

Offers a new theoretical framework for nonequilibrium critical phenomena.

Abstract

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.