7 problems

For a zero-temperature triangular-lattice Potts antiferromagnet on toroidal strips, let $q_0(L)$ and $q_2(L)$ be the relevant real crossings, and let $\ell$ denote the number of br…

For a zero-temperature square-lattice Potts antiferromagnet on toroidal strips, let $q$ be the Potts parameter, let $q_0(L)$ be the relevant real crossing, and let $\ell$ denote th…

Fix a theory in the family of $(0,1)$ $SO(n_3)$ gauge theories with parameters $(A,B,C)\in\mathbb{R}^3$. Consider the two regions of its classical phase diagram described in the pr…

Let $n\geq 0$, let $(g_c,\nu_c)$ denote the tricritical point, and let $C_{0,0}=(-\Delta_{{\mathbb Z}^3})^{-1}_{0,0}$. Define the open half-plane … For a point $(g,\nu)$ with…

Frieze medial space-filling conjecture. As $n\to\infty$, these curves become space-filling in this region. The claim is supported by the increasing density of the curves and the ob…

Consider the Potts model on an Archimedean lattice, with parameters $q$ and $v$, and let the BK phase denote the phase identified in the $(q,v)$ phase diagram. Archimedean-lattice…

The ruby lattice is studied through the Potts-model parameters $q$ and $v$, with $q_{\rm c}$ denoting the value of $q$ at which its Berker–Kadanoff (BK) phase terminates. Ruby-latt…