The pinning paths of an elastic interface

Abstract

We introduce a Markovian model describing the paths that pin an elastic interface moving in a two-dimensional disordered medium.The scaling properties of these “elastic pinning paths” (EPP) are those of a pinned interface belonging to the universality class ofthe Edwards-Wilkinson equation with quenched disorder. We find thatthe EPPare different from paths embedded on a directed percolation cluster,which are known to pin the interface of the “directed percolationdepinning” class of surface growth models.The EPP are characterized by a roughness exponent α = 1.25, intermediatebetween that of the free inertial process (α = 3/2) and thediode-resistor problem on a Cayley tree (α = 1). We also calculatenumerically the mean cluster size and the cluster size distribution forthe EPP.