  Monte Carlo simulations of the uniformly frustrated 3d XY model are used to
model vortex line fluctuations in high temperature superconductors in an
applied magnetic field. We find two distinct phase transitions. At a lower
T_{c\perp}, 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. Figures available upon request to
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