Phase transitions of hard disks in external periodic potentials: a Monte Carlo study

The nature of freezing and melting transitions for a system of hard disks in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants, etc., are used to map the phase diagram of the system for various values of the density and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of hard disks behaves in a fashion similar to charge-stabilized colloids that are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. Detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting.