The pinning paths of an elastic interface

Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA

Received: 21 November 1996
Accepted: 2 December 1997

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 of the Edwards-Wilkinson equation with quenched disorder. We find that the EPP are different from paths embedded on a directed percolation cluster, which are known to pin the interface of the “directed percolation depinning” class of surface growth models. The EPP are characterized by a roughness exponent , intermediate between that of the free inertial process () and the diode-resistor problem on a Cayley tree (). We also calculate numerically the mean cluster size and the cluster size distribution for the EPP.