13 problems

Determinant-asymptotics conjecture. The leading asymptotics is given by

Admissibility conjecture. If $G$ includes no oriented faces, then it is admissible.

Uniform bounds conjecture. There exist constants $0<c<C$, depending on all the data, such that $$

Orthogonality conjecture. In the limit $c\to\infty$,

Let $a_1,a_2,b_1,b_2,c_1,c_2$ be the six-vertex weights, let $\Delta$ be the associated interaction parameter, and consider the six-vertex model with domain wall boundary condition…

Fix the ratio $n/N$, where $n$ is the number of Bethe roots and $N$ is the system size, and let $C$ denote the contour described in the paper. Thermodynamic Bethe-root contour conj…

Let $n$ be the fixed number of Bethe roots, let $H$ be the parameter in the transfer matrix, and let $I_j$ denote the corresponding Bethe quantum numbers. Bethe quantum-number conj…

Let $\Lambda$ be a generic domain for the six-vertex model, and consider a south side ending at a corner, with the relevant external portion of the Arctic curve lying above that si…

Let $r(z)$ be the scaled logarithmic derivative of the boundary correlation function $h_N(z)$, namely … For the six-vertex model with domain wall boundary conditions, let $t$ and…

Let $q=1$, and impose stabilizing fixed boundary conditions producing an outer interface between the ferroelectric and disordered phases and an inner interface between the disorder…

Let $C$ be the smooth Bethe-root curve and define … Assume $\Delta\neq0$, and let $\alpha=n/N$ be fixed. Bethe-contour intersection conjecture. Exactly one of the following occurs:…

Let $N\to\infty$ and $n\to\infty$ with $\alpha=n/N$ fixed. Consider the Bethe equations for the six-vertex transfer matrix and the maximal eigenvalue in the subspace…

Let $H:\mathbb{R}^2\to\mathbb{R}$ be the scaling-limit function associated with the minimizer near a singular point of the minimal height function. The asymptotic structure conject…