3 problems

Let $q\geq 3$, $r\in \\{1,\dots,q-1\\}$, and consider the fuzzy Potts model on the torus $\mathbb{T}^d$. Denote by $J_c$ the critical value corresponding to non-uniqueness of Gibbs…

Let $J>0$, $q\geq 3$, and $r\in \\{1,\dots,q-1\\}$. Consider the fuzzy Potts model on the torus $\mathbb{T}^d$, and let $\gamma_p$ be Bernoulli product measure of density $p$. Defi…

Let $q\geq 3$, $r\in \\{1,\dots,q-1\\}$, and consider the fuzzy Potts model on $\mathbb{Z}^d$. For $J>0$, write $\nu_{q,J,r}^{\mathbb{Z}^d,+}$ for its plus-state fuzzy Potts measur…