Phase transitions and vortex-line entanglement in a model high-temperature superconductor.

We carry out Monte Carlo simulations of the uniformly frustrated three dimensional XY model, as a model for vortex line fluctuations in high temperature superconductors in an applied magnetic field. We show, comparing systems of different size, that there are two distinct phase transitions. At a lower Tc⊥, the vortex lattice melts, and coherence is lost in planes perpendicular to the magnetic field. At a higher Tcz, a vortex tangle percolates throughout the system, and coherence is lost parallel to the magnetic field. Cooling below Tcz, high energy barriers for vortex line cutting lead to an entangled glassy state. 74.60.Ge, 64.60-i, 74.40.+k Typeset using REVTEX