Direct test of defect-mediated laser-induced melting theory for two-dimensional solids

We investigate by direct numerical solution of appropriate renormalization flow equations the validity of a recent dislocation unbinding theory for laser-induced freezing and melting in two dimensions. The bare elastic moduli and dislocation fugacities are obtained for three different two-dimensional systems namely, the hard disk, inverse 12th power, and Derjaguin-Landau-Verwey-Overbeek potentials. A restricted Monte Carlo simulation sampling only configurations without dislocations is used to obtain these quantities. These are then used as inputs to the flow equations. Numerical solution of the flow equations then yields the phase diagrams. We conclude that (a) the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results, (b) there is excellent quantitative agreement between our results and earlier conventional Monte Carlo simulations for the hard disk system, and (c) while the qualitative form of the phase diagram is reproduced for systems with soft potentials there is some quantitative discrepancy which we explain.