Continuous Melting of a "Partially Pinned" Two-Dimensional Vortex   Lattice in a Square Array of Pinning Centers
  The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition. 
Toby Joseph and Chandan Dasgupta (Centre for Condensed Matter Theory,   Department of Physics, Indian Institute of Science, ...