  Using the theory of large deviations, we analyze the phase transition
structure of the Curie-Weiss-Potts spin model, which is a mean-field
approximation to the Potts model. This analysis is carried out both for the
canonical ensemble and the microcanonical ensemble. Besides giving explicit
formulas for the microcanonical entropy and for the equilibrium macrostates
with respect to the two ensembles, we analyze ensemble equivalence and
nonequivalence at the level of equilibrium macrostates, relating these to
concavity and support properties of the microcanonical entropy. The
Curie-Weiss-Potts model is the first statistical mechanical model for which
such a detailed and rigorous analysis has been carried out.
