Self-organized criticality in linear interface depinning and sandpile models

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.