VORTICES IN A THIN-FILM SUPERCONDUCTOR WITH A SPHERICAL GEOMETRY

We report results from Monte Carlo simulations of a thin-film supercon ductor in a spherical geometry within the lowest-landau-level approxim ation. We observe the absence of a phase transition to a low-temperatu re vortex solid phase with these boundary conditions; the system remai ns in the vortex liquid phase for all accessible temperatures. The cor relation lengths are measured for phase coherence and density modulati on. Both lengths display identical temperature dependences, with an as ymptotic scaling form consistent with a continuous zero-temperature tr ansition. This contrasts with the first-order freezing transition whic h is seen in the alternative quasiperiodic boundary conditions. The hi gh-temperature perturbation theory and the ground states of the spheri cal system suggest that the thermodynamic limit of the spherical geome try is the same as that on the flat plane. We discuss the advantages a nd drawbacks of simulations with different geometries, and compare wit h current experimental conclusions. The effect of having a large-scale inhomogeneity in the applied field is also considered.