On delocalization in the six-vertex model

Abstract

We show that the six-vertex model with parameter $c\in [\sqrt{3},2]$ on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreover we prove that for $c\in [\sqrt{2+\sqrt{2}},2]$, the associated height function on ${\mathbb{Z}}^2$ has unbounded variance. The proof relies on an extension of the Baxter-Kelland-Wu representation of the six-vertex model to multi-point correlation functions of the associated spin model. Other crucial ingredients are the uniqueness and percolation properties of the critical random cluster measure for $q\in [1,4]$, and recent results relating the decay of correlations in the spin model with the delocalization of the height function.

arXiv comment24 pages

References in corpus (2)

• Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le 4$
• Height fluctuations in interacting dimers

Cited by in corpus (5)

• On the transition between the disordered and antiferroelectric phases of the 6-vertex model
• Nonexistence and Uniqueness for Pure States of Ferroelectric Six-Vertex Models
• On antiferromagnetic regimes in the Ashkin-Teller model
• Weakly non-planar dimers
• On the duality between height functions and continuous spin models