The Depinning Transition

Abstract

Abstract Several systems in condensed matter physics can be described by elastic manifolds in random media. Concrete examples are provided by domain walls in ferromagnets, flux lines in type II superconductors, contact lines, crack fronts and dislocations. When an elastic manifold is pushed through a disordered landscape, it typically displays a depinning transition between a moving and a pinned phase. In the past decades, a vast theoretical effort has been devoted to understand the depinning transition as a non-equilibrium critical phenomenon. In the course of time, a deeper level of description and understanding of this phenomenon has been achieved, going far beyond a mere estimate of the depinning force, which has typically been the original motivation to address the problem. The morphology of a manifold is generally found to be self-affine and can be characterized by a roughness exponent. Other scaling exponents have been introduced to characterize the behavior of correlation lengths and times, the velocity above depinning. In addition, the dynamics of elastic manifolds proceeds by avalanches that are power law distributed at the depinning transition. Quantitative predictions of the critical exponents have been obtained analytically by the renormalization group and have been confirmed by numerical simulations.