Large Deviations and Equilibrium Macrostate Phase Transitions

The application of the aggregate path coupling method to prove rapid mixing takes advantage of large deviations estimates that these models satisfy. In this chapter, we first give a brief summary of large deviation theory used in this book, written in the context of Gibbs ensembles defined in Chapter 2 For a more complete theory of large deviations see for example [14] and [22]. We then define the set of equilibrium macrostates in terms of the large deviation principle upper bound, as originally defined in [24]. In Section 3.1, we define the types of phase transitions in terms of the sets of equilibrium macrostates and, in the following sections, we give descriptions of the phase transition behaviors of the four classes of models introduced in Chapter 2