Phase coexistence in Ising, Potts and percolation models (Q5954102)

Ising-Potts models and random cluster models on certain finite regions of the lattice \(Z^d\) are studied. The main goal of the work is to justify, starting from a microscopic point of view, the validity of the basic assumptions underlying the classical phenomenological theory of coexisting phases, namely, that the shapes of coexisting phases are governed by a variational principle. The various phases emerging in a model define a partition, called the empirical phase partition of the space. The main results are large deviation principles for the empirical phase partition. For the partition induced by large clusters in the Fortuin-Kasteleyn model and its transfer to the Ising-Potts model a general large deviation principle is established. For the empirical phase partition induced by the various phases a large deviation principle is obtained. These results are valid for temperatures \(T\) below a limit of slab-thresholds \(\widetilde T_c\) conjectured to agree with the critical point \(T_c\), and \(T\) should be such that there exists only one translation invariant infinite volume state in the corresponding Fortuin-Kasteleyn model.