Self-consistent theory of dynamic melting of a vortex lattice
  The dynamic melting of vortex lattices in type II superconductors is considered. A field-theoretic formulation of the pinning problem allows the average over the quenched disorder to be performed exactly. A self-consistent theory is constructed using a functional method for the effective action, allowing a determination of the pinning force and the vortex fluctuations. The phase diagram for the dynamic melting transition is determined numerically. In contrast to perturbation theory, the self-consistent theory is in quantitative agreement with the prediction of a recent phenomenological theory and simulations and experimental data. 
Staffan Grundberg and J{\o}rgen Rammer