MONTE-CARLO METHOD FOR A LATTICE SUPERCONDUCTOR WITH FREE SURFACES

We report a Monte Carlo (MC) method to simulate a lattice superconduct or in the shape of a slab with two plane interfaces, which are paralle l to each other and separating the superconductor from the vacuum. Thi s method is based on the lattice London model introduced by Carneiro, adapted here to the slab geometry. The energy of a vortex configuratio n is obtained from the exact solution of this model for uniaxial aniso tropy when the interfaces are either perpendicular or parallel to the axis of anisotropy. Besides the usual bulk vortex-vortex interactions, the energy has surface contributions that are similar to those derive d in continuum London theory for the same geometry. The MC procedure u ses vortex loops as the basic building block to generate vortex config urations, except at the interfaces where open vortex lines are used. T he latter are responsible for the penetration of vortex lines in the s lab's interior when an external field is applied parallel to the inter faces. Results of simulations for an isotropic superconducting slab ar e reported. It is found that the vortex lines that penetrate the slab, driven by the external field, form a vortex-line lattice at low tempe ratures. Melting and freezing of this lattice is studied in some detai l. The magnetization is studied as a function of the applied field and temperature. Evidence is found that is changes by a small amount acro ss the melting and freezing transitions.