Scaling in self-organized criticality from interface depinning?

TL;DR

This paper explores the connection between self-organized criticality (SOC) and interface depinning, providing a geometric framework to understand SOC avalanche exponents through a mapping to depinning models.

Contribution

It introduces a geometric description linking SOC models to interface depinning, clarifying how SOC ensembles differ and deriving avalanche exponents from depinning critical points.

Findings

Two main scaling regimes for SOC ensembles are identified.

Numerical simulations support the proposed geometric description.

SOC avalanche exponents can be derived from depinning universality classes.

Abstract

The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented first, to understand how to reach the SOC ensemble and the differences of this ensemble with the usual depinning scenario. In order to derive the SOC avalanche exponents from those of the depinning critical point, a geometric description is discussed, of the quenched landscape in which the 'interface' measuring the integrated activity moves. It turns out that there are two main alternatives concerning the scaling properties of the SOC ensemble. These are outlined in one dimension in the light of scaling arguments and numerical simulations of a sandpile model which is in the quenched Edwards-Wilkinson universality class.