  We consider the orientational alignment of dipoles due to strong matter light
coupling, for a non-vanishing density of excitations. We compare various
approaches to this problem in the limit of large numbers of emitters, and show
that direct Monte Carlo integration, mean-field theory, and large deviation
methods match exactly in this limit. All three results show that orientational
alignment develops in the presence of a macroscopically occupied polariton
mode, and that the dipoles asymptotically approach perfect alignment in the
limit of high density or low temperature.
