Mjw. Dodgson et Ma. Moore, VORTICES IN A THIN-FILM SUPERCONDUCTOR WITH A SPHERICAL GEOMETRY, Physical review. B, Condensed matter, 55(6), 1997, pp. 3816-3831
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.