Correlation lengths for vortex-liquid freezing in a model of layered high-temperature superconductor

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.