The pinning paths of an elastic interface

– 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 α = 1.25, intermediate between that of the free inertial process (α = 3/2) and the diode-resistor problem on a Cayley tree (α = 1). We also calculate numerically the mean cluster size and the cluster size distribution for the EPP. The problem of interface roughening in the presence of quenched disorder is a topic of recent interest, due to its importance as a paradigm in condensed-matter physics and due to the broad range of applications [1]. In a typical case, the interface moves in a (d+ 1)-dimensional disordered medium driven by a homogeneous force F . At small forces, the interface is pinned by the impurities of the medium, while the interface undergoes a depinning transition at a critical force Fc, and for F > Fc the interface moves with a nonzero velocity. The spatial fluctuations of the interface are characterized by the scaling of the saturated interface width Wsat(L) defined as the rms fluctuations of the interface height for a system size L,