Depinning free of the elastic approximation

Abstract

We model the isotropic depinning transition of a domain wall using a two-dimensional Ginzburg-Landau scalar field instead of a directed elastic string in a random media. An exact algorithm accurately targets both the critical depinning field and the critical configuration for each sample. For random bond disorder of weak strength Δ, the critical field scales as Δ4/3 in agreement with the predictions for the quenched Edwards-Wilkinson elastic model. However, critical configurations display overhangs beyond a characteristic length l0∼Δ-α, with α≈2.2, indicating a finite-size crossover. At large scales, overhangs recover the orientational symmetry which is broken by directed elastic interfaces. We obtain quenched Edwards-Wilkinson exponents below l0 and invasion percolation depinning exponents above l0. A full picture of domain-wall isotropic depinning in two dimensions is hence proposed.