Delocalization of the height function of the six-vertex model

Abstract

We show that the height function of the six-vertex model, in the parameter range $\mathbf{a}=\mathbf{b}=1$ and $\mathbf{c}\ge 1$, is delocalized with logarithmic variance when $\mathbf{c}\le 2$. This complements the earlier proven localization for $\mathbf{c}>2$. Our proof relies on Russo--Seymour--Welsh type arguments, and on the local behaviour of the free energy of the cylindrical six-vertex model, as a function of the unbalance between the number of up and down arrows.

55 pages, 16 figures

References in corpus (3)

• Discretely Holomorphic Parafermions and Integrable Loop Models
• Lectures on the integrability of the 6-vertex model
• Rotational invariance in critical planar lattice models

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• The Discrete Gaussian model, I. Renormalisation group flow at high temperature
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• On the duality between height functions and continuous spin models