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 $Δ= 0$, the fluctuations of the e...
| Main Authors: | , , |
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| Format: | Text |
| Language: | unknown |
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arXiv
2023
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2303.14669 https://arxiv.org/abs/2303.14669 |
| Summary: | 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 $Δ= 0$, 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 $Δ$ ($0\leq Δ< 1$). 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. ... : 15 pages, 9 figures, revised version: added the study of the third and fourth cumulant. J. Phys. A: Math. Theor. (2023) ... |
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