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 \left[\sqrt{2 + \sqrt{2}}, 2 \right]$, 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.

mathematical physicsgeneral mathematicsprobability

Audience: researchers in the topic

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Portsea Maths Research Webinar

Series comments: The theme for June is "Probability theory and related fields". The theme for July is "Linear algebra and its applications". There are no webinars in August.