The Arctic Curve Conjecture for the six-vertex model on the square domain

Let $r(z)$ be the scaled logarithmic derivative of the boundary correlation function $h_N(z)$, namely

$$r(z):=\lim_{N \to \infty}\frac{1}{N}z\frac{\mathrm{d}}{\mathrm{d} z}\ln h_N(z).$$

For the six-vertex model with domain wall boundary conditions, let $t$ and $\Delta$ be the model parameters, and let $x$ and $y$ denote rescaled coordinates in the square domain. Arctic Curve Conjecture. The south-east arc of the Arctic curve can be expressed parametrically as $x=x(z)$, $y=y(z)$, with $z \in [1,+\infty)$, by the simultaneous equations

$$F(x,y;z)=0,\qquad \frac{\mathrm{d}}{\mathrm{d}z}F(x,y;z)=0,$$

where

$$F(x,y;z)=x-\frac{z(t^2-2\Delta t+1)}{(z-1)(t^2z-2\Delta t+1)}y-r(z).$$

This gives the envelope of the tangent lines determined by the boundary correlation function and is the EFP/Tangent Method description of the Arctic curve. The conjectural status concerns the validity of this construction beyond the settings where the underlying asymptotic assumptions have been established.