  The nature of freezing and melting transitions for a system of model colloids
interacting by a DLVO potential in a spatially periodic external potential is
studied using extensive Monte Carlo simulations. Detailed finite size scaling
analyses 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 reduced screening length $\kappa a_{s}$ 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 soft 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.
