Models of flux pinning in the quasistatic limit

The deformations of a two-dimensional vortex lattice pinned by a random pinning potential are studied with use of a molecular-dynamics--annealing method. We find that the response of the lattice varies as a function of the strength of the random potential. For the weakest potentials, the response of the lattice is entirely elastic. For somewhat stronger random potentials, elastic instabilities are induced in the lattice. Further increases in the random potential induce a highly defective lattice, consisting of trapped lattice regions separated by areas in which the lattice flows plastically. By examining the finite-size-scaling behavior of the lattice we conclude that the elastic response is an artifact of the finite size of the simulations and that the strength of the random potential at which the response of the lattice changes from elastic instability to plastic flow goes as 1/ln(Nᵥ), where Nᵥ is the number of vortices in the simulation. Our simulation results are not well described by the theory of Larkin and Ovchinnikov.