Large Deviation Behavior of Statistical Mechanics Models in the Multiphase Regime

The theory of large deviations was initiated by the study of the asymptotical behavior of probabilities of large deviations of sums of n identically distributed independent random variables. In this case the logarithms of the probabilities are asymptotically equal to -nI, where I is a constant which can be defined by a minimization of the so-called action functional. The theory of large deviations is now a well-developed branch of the probability theory (see the books [1], [2] for example) devoted mainly to generalization of the mentioned asymptotics to wide classes of random processes. Also these types of results were recently generalized on a wide class of Gibbsian random fields (see [3], [4]).