Stable and Metastable Phases for the Curie–Weiss–Potts Model in Vector-Valued Fields via Singularity Theory

We study the metastable minima of the Curie–Weiss Potts model with three states, as a function of the inverse temperature, and for arbitrary vector-valued external fields. Extending the classic work of Ellis and Wang (Stoch Process Appl 35(1):59–79, 1990) and Wang (Stoch Process Appl 50(2):245–252, 1994) we use singularity theory to provide the global structure of metastable (or local) minima. In particular, we show that the free energy has up to four local minimizers (some of which may at the same time be global) and describe the bifurcation geometry of their transitions under variation of the parameters.