Phase transitions in model colloids in reduced geometry

The nature of the melting transition for a system of hard disks with translational degrees of freedom in two spatial dimensions has been analyzed by a novel finite size scaling technique. The behavior of the system is consistent with the predictions of the KTHNY theory. Hard and soft disks in external periodic potentials show rich phase diagrams including freezing and melting transitions when the density of the system is varied. Here we report on extensive Monte Carlo simulations for detailed finite size scaling analyses of various thermodynamic quantities like the order parameter, its cumulants, etc. in order to map the phase diagram of the system for various values of the density and the amplitude of the external potential. For hard disks we find clear indication of a re-entrant 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 which are known to undergo an initial freezing, followed by a re-melting 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. The differences and similarities of systems with soft potentials (DLVO, 1/r12) is discussed.