Elastic Depinning Transition

Elastic manifold driven over random disorder: avalanches and critical force

Force F: 0.00 F_c: — Velocity v: 0.000 Avalanche size: 0 Phase: pinned
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Elastic depinning (Fisher 1985, Narayan-Fisher 1993): A d-dimensional elastic manifold (interface, domain wall, vortex lattice) driven through a medium with random quenched disorder undergoes a non-equilibrium phase transition at a critical force F_c. Below F_c: the manifold is pinned — static or creeping via thermal activation. Above F_c: the manifold flows with mean velocity v ~ (F−F_c)^β (β≈0.63 in 1D). Near F_c, the dynamics is governed by avalanches — sudden jumps where a segment depins and triggers neighbors via elastic coupling. Avalanche sizes S follow a power law P(S) ~ S^(−τ) with τ≈1.1 (mean-field: τ=3/2). This is the ABBM model (Alessandro-Beatrice-Bertotti-Montorsi 1990). Applications: Barkhausen noise (domain walls), earthquake faults, contact-line dynamics, CDW transport.