  Systems of coupled photonic cavities have been predicted to exhibit quantum
phase transitions by analogy with the Hubbard model. To this end, we have
studied topologies of few (up to six) photonic cavities each containing a
single two-level system. Quantum phase space diagrams are produced for these
systems, and compared to mean-field results. We also consider finite effective
temperature, and compare this to the notion of disorder. We find the extent of
the Mott lobes shrink analogously to the conventional Bose-Hubbard model.
