Fluctuation of the phase boundary in the six-vertex model with domain wall boundary conditions: a Monte Carlo study
Abstract We consider the six-vertex model with domain wall boundary conditions in a square lattice of dimension N × N . 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 <?CDATA $\Del...
| Published in: | Journal of Physics A: Mathematical and Theoretical |
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| Main Authors: | , , |
| Format: | Article in Journal/Newspaper |
| Language: | unknown |
| Published: |
IOP Publishing
2023
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1088/1751-8121/ad0a43 https://iopscience.iop.org/article/10.1088/1751-8121/ad0a43 https://iopscience.iop.org/article/10.1088/1751-8121/ad0a43/pdf |
| Summary: | Abstract We consider the six-vertex model with domain wall boundary conditions in a square lattice of dimension N × N . 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 <?CDATA $\Delta = 0$?> 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 ( <?CDATA $0\unicode{x2A7D} \Delta \lt 1$?> 0 ⩽ Δ < 1 ). We argue that the typical width of the fluctuations of the extremal path about the arctic curves scales as <?CDATA $N^{1/3}$?> N 1 / 3 and provide a numerical estimate for the parameters of the scaling random variable. |
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