The Low-Field Critical End Point of the First Order Transition Line in   YBCO
  We report on simulations of the first order phase transition in YBCO using the Lawrence-Doniach model. We find that the magnetization discontinuity vanishes and the first order transition line ends at a critical end point for low magnetic fields in agreement with experiment. The transition is not associated with vortex lattice melting, but separates two vortex liquid states characterized by different degrees of short-range crystalline order and different length scales of correlations between vortices in different layers. 
A. K. Kienappel and M. A. Moore