Self-organized criticality in linear interface depinning and sandpile models

TL;DR

This paper investigates the critical behavior of elastic interface models under disorder and driving forces, revealing a new universality class distinct from constant force models through perturbation theory and renormalization group analysis.

Contribution

It introduces a new universality class for interface depinning models, including sandpile and extremal dynamics, using analytical methods up to first order in 4-d.

Findings

Identifies critical phase in double limit of epsilon and c/epsilon

Establishes a new universality class for certain sandpile and interface models

Derives scaling exponents using perturbation theory and renormalization group

Abstract

The dynamics of an elastic interface profile h(x,t) under a driving force increasing at rate c, a restored force -epsilon h, and disorder is investigated. Using perturbation theory and functional renormalization group the phase diagram and the scaling exponents, up to the first order in 4-d, are obtained. The model is found to be critical in the double limit epsilon->0$ and c/epsilon->0$ and belongs to a different universality class as that of constant force models. It is shown that undirected sandpile models with stochastic rules and linear interface models with extremal dynamics belong to this new universality class.