  We present results from extensive numerical simulations on the
Lawrence-Doniach model within the lowest Landau level approximation in the
unconventional spherical geometry. We study the in-layer pancake vortex
density-density correlation function (intra-layer structure factor) and the
layer-to-layer order-parameter correlation function along the direction
perpendicular to the layers. Our results show strong evidence for the existence
of a single first-order phase transition at which both inter-layer coupling and
appearance of crystalline order in the in-layer vortex correlations take place
as temperature is lowered.
