9 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…

Let $T_{L,L}$ be the diagonal transfer-matrix sub-block for a triangular-lattice strip of width $L$ with fully toroidal boundary conditions, and let $b^{(L)}_1$ denote the stated a…

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 $c=e^{-2\beta H}$ and $d=e^{-2\beta J}$, and consider the one-dimensional 3-permaspin model with couplings $J$ and $H$. Let $z$ be the unique root of the cubic … whose argument…

Let $L\geqslant 1$, let $u_1,\dots,u_L$ be inhomogeneity parameters, and define the inhomogeneous open-boundary transfer matrix … where $K^-(u)=K(u)$, $K^+(u)=K(u+2\eta)$, … … Set…

For an $L_v\times L_h$ lattice at $z=-1$, let $G^{CC}_{L_h}$ and $G^{CF}_{L_h}$ be the generating functions along the periodic direction for the torus and cylinder, respectively, a…

Linear-coefficient conjecture. Both displayed expansions hold. The coefficients have been checked computationally in the ranges reported in the paper, and the relations among the a…

Free-energy expansion conjecture. The two displayed asymptotic expansions hold. This has been verified for $m\le 10$ using the explicitly computed polynomials $C_1,\ldots,C_{10}$.…