Self-organized criticality and interface depinning transitions

TL;DR

This paper explores the connection between self-organized criticality and interface depinning transitions by mapping sandpile models to driven interfaces, providing a continuum description and insights into different criticality approaches.

Contribution

It introduces a continuum framework linking sandpile models to interface depinning, revealing new scaling relations and criticality mechanisms.

Findings

Derived a scaling relation for the correlation length exponent in sandpiles.

Established equivalence between self-organized criticality and depinning transitions.

Provided a unified description for various criticality tuning methods.

Abstract

We discuss the relation between self-organized criticality and depinning transitions by mapping sandpile models to equations that describe driven interfaces in random media. This equivalence yields a continuum description and gives insight about various ways of reaching the depinning critical point: slow drive (self-organized criticality), fixed density simulations, tuning the interface velocity (extremal drive criticality), or tuning the driving force. We obtain a scaling relation for the correlation length exponent for sandpiles.