Potts and random cluster measures on locally regular-tree-like graphs

Anirban Basak, Amir Dembo, Allan Sly

Fixing $\beta \ge 0$ and an integer $q\ge 2$, consider the ferromagnetic $q$-Potts measures ${\mu }_n^{\beta ,B}$ on finite graphs ${\mathsf{G}}_n$ on $n$ vertices, with external field strength $B \g…