Metastability of Non-reversible, Mean-Field Potts Model with Three Spins

We examine a non-reversible, mean-field Potts model with three spins on a set with N↑∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\uparrow \infty $$\end{document} points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields, and it can be carried out in the case where the external field is in the direction or in the opposite direction to one of the values of the spins. Numerical computations permit to identify other phenomena which are not present in the previous situations.