Gaussian free field convergence of the six-vertex model with $-1\leqΔ\leq-\frac12$
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| Format: | Preprint |
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2026
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| _version_ | 1866911493201592320 |
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| author | Duminil-Copin, Hugo Kozlowski, Karol Kajetan Lammers, Piet Manolescu, Ioan |
| author_facet | Duminil-Copin, Hugo Kozlowski, Karol Kajetan Lammers, Piet Manolescu, Ioan |
| contents | We study the isotropic six-vertex model on $\mathbb{Z}^2$ with spectral parameter $Δ\in[-1,-1/2]$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gaussian free field convergence of the six-vertex model with $-1\leqΔ\leq-\frac12$ Duminil-Copin, Hugo Kozlowski, Karol Kajetan Lammers, Piet Manolescu, Ioan Mathematical Physics Probability Exactly Solvable and Integrable Systems We study the isotropic six-vertex model on $\mathbb{Z}^2$ with spectral parameter $Δ\in[-1,-1/2]$, 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. |
| title | Gaussian free field convergence of the six-vertex model with $-1\leqΔ\leq-\frac12$ |
| topic | Mathematical Physics Probability Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.06268 |