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Domain wall fluctuations of the six-vertex model at the ice point

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arxiv 2305.09502 v2 pith:J4PFHENV submitted 2023-05-16 cond-mat.stat-mech

Michael Praehofer , Herbert Spohn This is my paper · ORCID
classification cond-mat.stat-mech
keywords boundaryconditionsdomainfluctuationslinemodelpointsix-vertex
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abstract

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.

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Cited by 1 Pith paper

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  1. Frozen-corner enumeration of Alternating Sign Matrices

    math.CO 2025-09 conditional novelty 3.0 of 10

    The number of ASMs with an s by s frozen zero corner is conjectured to equal A_n det(1-M), a determinant formula verified numerically for all n up to 20.

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