6 problems

The Ashkin–Teller model on a box $\Lambda_n$ has configurations $(\sigma_1,\sigma_2):\Lambda_n\to\{-1,+1\}^2$ with density proportional to … On the self-dual line, assume $J\geq0$,…

Thermodynamic limit of the random-cluster partition function. As $n\rightarrow\infty$,

The bunkbed graph $G=(V,E)$ of a graph $\widetilde{G}=(\widetilde{V},\widetilde{E})$ is formed by superposing two identical copies of $\widetilde{G}$ and adding edges between corre…

Let $q>0$ and let $(\mathbb{G}_n)$ be a sequence of infinite transitive graphs converging locally to an infinite transitive graph $\mathbb{G}$. For an infinite transitive graph…

Let $q\in[0,4]$, and consider the random cluster model on lattice domains. For the Ising model, let $F(z)$ denote the function in Proposition, which is discrete holomorphic and sat…

Let $q\in[0,4]$, and consider the Fortuin–Kasteleyn random-cluster model on the square lattice at the self-dual value $p_{\mathrm{sd}}=\sqrt q/(\sqrt q+1)$, with Dobrushin boundary…