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 T(c perpendicular-to), the vortex lattice melts, and coherence is lost in planes perpendicular to the magnetic field. At a higher T(cz), a vortex tangle percolates throughout the system, and coherence is lost parallel to the magnetic field. Cooling below T(cz), high-energy barriers for vortex-line cutting lead to an entangled glassy state.