Fluctuation of the phase boundary in the six-vertex model with Domain Wall Boundary Conditions: a Monte Carlo study

We consider the six-vertex model with Domain Wall Boundary Conditions on a $N\times N$ square lattice. Our main interest is the study of the fluctuations of the extremal lattice path about the arctic curves. We address the problem through Monte Carlo simulations. At $\mathrm{\Delta }=0$, the fluctuations of the extremal path along any line parallel to the square diagonal were rigorously proven to follow the Tracy-Widom distribution. We provide strong numerical evidence that this is true also for other values of the anisotropy parameter $\mathrm{\Delta }$ ($0\le \mathrm{\Delta }<1$). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales as $N^{1\mathrm{/}3}$ and provide a numerical estimate for the parameters of the scaling random variable.