  Microcavity polaritons, which at low temperatures can condense to a
macroscopic coherent state, possess a polarization degree of freedom. This
article discusses the phase diagram of such a system, showing the boundaries
between differently polarized condensates. The Bogoliubov approximation is
shown to have problems in describing the transition between differently
polarized phases; the Hartree-Fock-Popov approximation performs better, and
compares well to exact results that can be used in the limit where the left-
and right-circular polarization states decouple. The effect on the phase
boundary of various symmetry breaking terms present in real microcavities are
also considered.
