THE PINNING PATHS OF AN ELASTIC INTERFACE

We introduce a Markovian model describing the paths that pin an elasti c interface moving in a two-dimensional disordered medium. The scaling properties of these ''elastic pinning paths'' (EPP) are those of a pi nned interface belonging to the universality class of the Edwards-Wilk inson equation with quenched disorder. We find that the EPP are differ ent from paths embedded on a directed percolation cluster, which are k nown to pin the interface of the ''directed percolation depinning'' cl ass of surface growth models. The EPP are characterized by a roughness exponent alpha = 1.25, intermediate between that of the free inertial process (alpha = 3/2) and the diode-resistor problem on a Cayley tree (alpha = I). We also calculate numerically the mean cluster size and the cluster size distribution for the EPP.