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arXiv · 2303.14669

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

Ivar Lyberg·Vladimir Korepin·Jacopo Viti
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Abstract

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 $\Delta = 0$, 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 $\Delta$ ($0\leq \Delta < 1$). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales as $N^{1/3}$ and provide a numerical estimate for the parameters of the scaling random variable.

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Ivar Lyberg, Vladimir Korepin, Jacopo Viti. 2023-03-26. Fluctuation of the phase boundary in the six-vertex model with Domain Wall Boundary Conditions: a Monte Carlo study. https://doi.org/10.1088/1751-8121/ad0a43.

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