2 problems

Let $m,k\geq 2$, $J>0$, and $\beta\geq 0$. A translation-invariant splitting Gibbs measure is a Gibbs measure invariant under the tree translations. Antiferromagnetic uniqueness co…

Let $G$ be a graph, let $d_v\coloneqq\deg_G(v)$, and let $H$ be an edge-weighted graph, possibly with loops. Define the weighted homomorphism count by … where $H(a,b)$ is the edge…