Molecular Dynamics of pancake vortices with realistic interactions:   Observing the vortex lattice melting transition
  In this paper we describe a version of London Langevin molecular dynamics simulations that allows for investigations of the vortex lattice melting transition in the highly anisotropic high-temperature superconductor material Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We include the full electromagnetic interaction as well as the Josephson interaction among pancake vortices. We also implement periodic boundary conditions in all directions, including the z-axis along which the magnetic field is applied. We show how to implement flux cutting and reconnection as an analog to permutations in the multilevel Monte Carlo scheme and demonstrate that this process leads to flux entanglement that proliferates in the vortex liquid phase. The first-order melting transition of the vortex lattice is observed to be in excellent agreement with previous multilevel Monte Carlo simulations. 
Yadin Y. Goldschmidt