8 problems

Let $m$ be the lattice-width parameter, let $q$ be the Potts-model state parameter, and let $\lambda_{\star,=}(m)$ and $\lambda_{\star,\neq}(m)$ denote the dominant transfer-matrix…

Potts monotonicity conjecture. If reconstruction is solvable for $M_1$, then it is also solvable for $M_2$.

Consider the symmetric Potts channel $M$ on $q\geq 3$ symbols, with $b$-ary tree branching factor $b$ and second eigenvalue $\lambda_2(M)$. Potts-model below-bound conjecture. Ther…

Let $L$ be the width of a triangular-lattice strip with cylindrical boundary conditions, let $B_k$ denote the Beraha numbers, and let $D(q)$ be the amplitude matrix. Cylindrical-st…

Let $L$ be the width of a triangular-lattice strip with free, cylindrical or “zig-zag” boundary conditions. Let $B_2,\ldots,B_{L+1}$ be the corresponding Beraha numbers, let…

Let $\nu=\nu(\beta,q,d)$ be Potts lattice gauge theory on $\mathbb{Z}^d$. Let $\sigma_N=[0,1]^2\times\{N\}\times\{0\}$ be a plaquette, and for a plaquette $\sigma$ let…

Let $G$ be a random $\Delta$-regular bipartite graph, and let $Z_{G,q}(\beta)$ be the partition function of the anti-ferromagnetic $q$-state Potts model on $G$. Random-regular-grap…

Let $G$ be a random $\Delta$-regular bipartite graph on $2n$ vertices, let $\mu_{G,q;\beta}$ be the anti-ferromagnetic $q$-state Potts Gibbs distribution, and let an FPAUS mean a f…