Monte Carlo investigation of the properties of the vortex liquid in two-dimensional superconductors

A Monte Carlo simulation of a type-II superconductor in a magnetic field is used to calculate the entropy and specific heat, in the two-dimensional geometries of both the plane and the surface of a sphere. In addition the structure factor of the vortices on the sphere is calculated, which gives a measurement of the correlation length associated with triangular-lattice ordering of the vortices. This length scale is found to diverge only in the zero-temperature limit, in the same way as the correlation length associated with phase coherence (off-diagonal long-range order) of the system, as calculated by a scaling argument based on phase fluctuations. This provides strong evidence against the formation of the Abrikosov-vortex-lattice phase below a finite transition temperature. The Monte Carlo calculations of the structure factor in the high-temperature (vortex-liquid) limit are found to be in good agreement with analytic results.