Density-functional theory of freezing of vortex-liquid in quasi   two-dimensional superconductors
  We present a theory of vortex liquid-to-solid transition in homogeneous quasi 2D superconductors. The free energy is written as a functional l of density of zeroes of the fluctuating order parameter. The transition is weakly first-order and well below the Hc2(T) line. Transition temperature, discontinuities of the average Abrikosov ratio and of the average superfluid density, the Debay-Waller factor and the latent heat are in good agreement with Monte Carlo simulations. The density is only weakly modulated in the "vortex-solid" phase, consistent with the density-wave behavior. 
Igor Herbut and Zlatko Tesanovic