Vortices in a thin-film superconductor with a spherical geometry

We report results from Monte Carlo simulations of a thin-film superconductor in a spherical geometry within the lowest-Landau-level approximation. We observe the absence of a phase transition to a low-temperature vortex solid phase with these boundary conditions; the system remains in the vortex liquid phase for all accessible temperatures. The correlation lengths are measured for phase coherence and density modulation. Both lengths display identical temperature dependences, with an asymptotic scaling form consistent with a continuous zero-temperature transition. This contrasts with the first-order freezing transition which is seen in the alternative quasiperiodic boundary conditions. The high-temperature perturbation theory and the ground states of the spherical system suggest that the thermodynamic limit of the spherical geometry is the same as that on the flat plane. We discuss the advantages and drawbacks of simulations with different geometries, and compare with current experimental conclusions. The effect of having a large-scale inhomogeneity in the applied field is also considered.