  A system of coupled photonic cavities on a two-dimensional square lattice is
systematically investigated using the stochastic series expansion quantum Monte
Carlo method. The ground state phase diagram contains insulating phases with
integer polariton densities surrounded by a superfluid phase. The finite-size
scaling of the superfluid density is used to determine the phase boundaries
accurately. We find that the critical behavior is that of the generic,
density-driven Mott-superfluid transition with dynamic exponent $z=2$, with no
special multicritical points with $z=1$ at the tips of the insulating-phase
lobes (as exist in the case of the Bose-Hubbard model). This demonstrates a
limitation of the description of polaritons as structureless bosons.
