Size driven phase transitions in pinned vortex systems
  We model a tridimensional vortex system in a sample with square superficial pinning in the top surface and obtain the ground state structures as a function of the sample thickness. Using a simple Frenkel-Kontorova like model and no adjustable parameters, we reproduce the experimental vortex configurations seen in the bottom surface and their range of stability. We find three phases with two transitions between them, including a continuous one from square to distorted hexagonal structure and a discontinuous one from distorted hexagonal to hexagonal structure. 
P. S. Cornaglia and M. F. Laguna