  In this survey paper, we describe and characterize an extension to the
classical path coupling method applied statistical mechanical models, referred
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.
