  We report on Monte-Carlo simulations of the six-vertex model with domain wall
boundary conditions. In thermal equilibrium such boundary conditions force a
fluctuating line separating the disordered region from the perfectly ordered
ones. Specifically we study the ice point at which all vertex weights are
equal. With high precision the one-point fluctuations of the line are confirmed
to be of order $N^{1/3}$ and governed by the Tracy-Widom distribution.
Furthermore, the non-universal scaling coefficients are computed for a wide
range of interaction strengths. A draft of this paper was completed in January
2019. We improved the presentation and updated references.
