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arXiv · 2603.06268

Gaussian free field convergence of the six-vertex model with $-1\leq\Delta\leq-\frac12$

Hugo Duminil-Copin·Karol Kajetan Kozlowski·Piet Lammers·Ioan Manolescu
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Abstract

We study the isotropic six-vertex model on $\mathbb{Z}^2$ with spectral parameter $\Delta\in[-1,-1/2]$, that is, with weights $\mathbf{a}=\mathbf{b}=1$ and $\mathbf{c}\in[\sqrt{3},2]$. We show that the associated height function converges, in the scaling limit, to a properly scaled full-plane Gaussian free field. The result extends to anisotropic weights $\mathbf{a}\neq\mathbf{b}$ upon using a suitable embedding of the lattice.

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Hugo Duminil-Copin, Karol Kajetan Kozlowski, Piet Lammers, Ioan Manolescu. 2026-03-06. Gaussian free field convergence of the six-vertex model with $-1\leq\Delta\leq-\frac12$. https://arxiv.org/abs/2603.06268

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