5 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 $J\geq0$,…

Conformal-invariance conjecture. The collections $\Gamma_n$ converge in distribution to $\Gamma$ with respect to the metric $d_{\mathfrak{L}}$. This conjecture describes the expect…

Let $q\in (0,4]$ and let … Suppose that $D$ is a Jordan domain, $\epsilon_n\to 0$ as $n\to\infty$, and that $\mathcal{D}_n$ is a discrete domain in $\epsilon_n\mathbb{Z}^2$ for eac…

Condition on the event $|{\bf t}(r)|=n$, and let ${\sf Canonical}({\bf t}^{<n}(r))$ be the canonical embedding of the root component obtained by edge evaporation. The massive…

Loop-cluster metric conjecture. There is a metric on the clusters of $\mathcal{L}_{g,1/2}$ inside $\Sigma$, measurable with respect to $\mathcal{L}_{g,1/2}$, obtained as the limit…