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.

7 pages, 4 figures