  In this paper, we present a novel extension to the classical path coupling
method to statistical mechanical models which we refer to as aggregate path
coupling. In conjunction with large deviations estimates, we use this aggregate
path coupling method to prove rapid mixing of Glauber dynamics for a large
class of statistical mechanical models, including models that exhibit
discontinuous phase transitions which have traditionally been more difficult to
analyze rigorously. The parameter region for rapid mixing for the generalized
Curie-Weiss-Potts model is derived as a new application of the aggregate path
coupling method.
