  We investigate by direct numerical solution of appropriate renormalization
flow equations, the validity of a recent dislocation unbinding theory for laser
induced freezing/melting in two dimensions. The bare elastic moduli and
dislocation fugacities which are inputs to the flow equations are obtained for
three different 2-d systems (hard disk, inverse $12^{th}$ power and the
Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo
simulation sampling only configurations {\em without} dislocations. 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.
