2 problems

Let $\Pi=\{x\in\mathbb{Z}^d:x_1\geq 0\}$ be a half-space, and let $\Lambda'_n\supset\{-n,\ldots,n\}^d$ satisfy … Fix boundary conditions $\tau$ equal to $0$ on $\Pi$ and $1$ on…

Let the $3$-state antiferromagnetic Potts model be defined on the bipartite lattice $\mathbb{Z}^d$, with configurations assigning one of three states to each vertex and Hamiltonian…