Vortex-line fluctuations in model high-temperature superconductors

We carry out Monte Carlo simulations of the uniformly frustrated three-dimensional XY model, as a model for vortex-line fluctuations in a high-${\mathit{T}}_{\mathit{c}}$ superconductor in an external magnetic field. A density of vortex lines of f=1/25 is considered. We find two sharp phase transitions. The low-T superconducting phase is an ordered vortex-line lattice. The high-T normal phase is a vortex-line liquid, with much entangling, cutting, and loop excitations. An intermediate phase is found, which is characterized as a vortex-line liquid of disentangled, approximately straight, lines. In this phase, the system displays superconducting properties in the direction parallel to the magnetic field, but normal behavior in planes perpendicular to the field. A detailed analysis of the vortex structure function is carried out.