  We study the phenomenon of laser induced freezing, within a numerical
renormalization scheme which allows explicit comparison with a recent defect
mediated melting theory. Precise values for the `bare' dislocation fugacities
and elastic moduli of the 2-d hard disk system are obtained from a constrained
Monte Carlo simulation sampling only configurations {\em without} dislocations.
These are used as inputs to appropriate renormalization flow equations to
obtain the equilibrium phase diagram which shows excellent agreement with
earlier simulation results. We show that the flow equations need to be correct
at least up to third order in defect fugacity to reproduce meaningful results.
