  We report on a Monte Carlo study of the lowest-Landau-level limit of the
Lawrence-Doniach model for a layered superconductor. We have studied order
parameter correlation functions for indications of the broken translational
symmetry and the off-diagonal long range order present in the mean-field-theory
vortex lattice. Our results are consistent with a single first order phase
transition between a low temperature 3D vortex solid phase, with both broken
translational symmetry and off-diagonal long range order, and a high
temperature vortex liquid phase with no broken symmetries. We construct a
universal phase diagram in terms of dimensionless parameters characterizing
intra-layer and inter-layer couplings. The universal phase boundary extracted
from our simulations and the associated latent heats and magnetization jumps
are compared with experiment and with numerical results obtained for related
models.
