Simple Model of Superconducting Vortex Avalanches

We introduce a simple lattice model of superconducting vortices driven by repulsive interactions through a random pinning potential. The model describes the behavior at the scale of the London length λ or larger. It self-organizes to a critical state, characterized by a constant flux density gradient, where the activity takes place in terms of avalanches spanning all length scales up to the system size. We determine scaling relations as well as four universal critical exponents for avalanche moments and durations: τ = 1.63+/-0.02, D = 2.7+/-0.1, z = 1.5+/-0.1, and τ_t = 2.13+/-0.14, for the system driven at the boundary.