Phase transitions in isotropic extreme type-II superconductors

Using large-scale Monte Carlo simulations on a uniformly frustrated three-d imensional XY model, we report a first-order vortex lattice melting transit ion in clean, isotropic extreme type-II (kappa-->infinity) superconductors. This work clarifies an important issue: the unpinned vortex liquid is alwa ys incoherent with no phase coherence in any direction for all anisotropies . Previous claims of a disentangled vortex liquid for isotropic superconduc tors based on simulations are due to finite-size effects. We explicitly sho w that the effective vortex-line tension vanishes precisely at the supercon ducting phase transition in zero magnetic field. This loss of line tension is accompanied by an abrupt change in the connectivity of the vortex tangle across the superconductor. We also obtain results indicating that the conn ectivity of the vortex tangle changes in a similar way even in a finite mag netic field, and suggest that this could also be associated with a genuine phase transition. [S0163-1829(99)14721-0].