5 problems

Consider the Lee–Yang zeros of the finite-volume partition function of the Ising model, and take the thermodynamic limit as the finite domain grows. Lee–Yang conjecture. In the the…

Nishimori–Griffiths conjecture. All principal zeros decrease as $t$ varies over $t>0$.

Let $G=(V,E)$ be a finite graph, let $mathbf{J}=(J{uv}){uv ein E}$ be ferromagnetic pair interactions, and let $h einmathbb{C}$ be a uniform external field. Define the Ising partit…

Let $d\geq 2$ be an integer, let $b\in\left(\frac{d-1}{d+1},1\right)$ be rational, and let $\mathbb{S}_{\mathbb{Q}}(d,b)$ denote the set of rational points…

Let $\Delta\geq 3$ be an integer, let $b\in\left(\frac{\Delta-2}{\Delta},1\right)$ be rational, and let $\lambda\in\mathbb{S}_{\mathbb{Q}}$ be non-real. Let…