The conjectural determinant asymptotics for the 6V' model

Let

$$be the parameter in the disordered regime, and let$$

be the determinant associated with the 6V' model, with spectral parameters $u$ and $v$. Define the leading asymptotic quantity by

$$W[u,v]=\lim_{N\to\infty}\Delta_N[u,v]^{-\frac{1}{N^2}}.$$

Determinant-asymptotics conjecture. The leading asymptotics is given by

$$W[u,v]=\frac{\sin(\alpha(u-v-\eta))\,\sin(\alpha(-u-v-\eta))}{\alpha\,|\sin(2\alpha u)\,\sin(2\alpha(v+\eta))|^{\frac{1}{2}}},$$

where

$$\alpha=\frac{\pi}{\pi-2\eta}.$$

The formula agrees with the exact classical limit $=0$ and free-fermion limit $=\frac{\pi}{4}$, and the subsequent discussion gives further checks, but the general determinant asymptotics remains conjectural.