Work

Conformal invariance of the six-vertex model's height function

Year: 2026

Type: preprint

Abstract: In this paper, we show that the height function of the six-vertex model in simply connected domains with piecewise constant boundary conditions converges to the Gaussian Free Field (GFF) with Dirichlet boundary conditions. This implies the conformal invariance of the scaling limit of the model. The argument relies on the full plane GFF convergence combined with Reflexion Positivity and qualitative estimates. The proof works for a wide range of spectral parameters $Δ$ (among which $Δ$ close to $0$, and between $-1$ and $-1/2$) making this paper the first instance of a conformal invariance result for a continuum of models. The paper has consequences for other models, including the FK percolation with cluster-weight $q=4$ and the Ashkin-Teller model, which we will pursue in future work.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.07454

Authors: Averous, Emile, Duminil-Copin, Hugo, He, Tiancheng, Lammers, Piet, Manolescu, Ioan

Institutions: University of Geneva, Institut des Hautes Études Scientifiques, Centre National de la Recherche Scientifique, Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation, University of Fribourg

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Centres of Competence in Research SwissMAP, Agence Nationale de la Recherche, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: G7080048889

OpenAlex ID: W7220909819

Cites: 6

Cited by: 1

Related to: 10