On Delocalization in the Six-Vertex Model

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 size of grows to infinity. Moreover we prove for $c\in[\sqrt{2+\sqrt 2}, 2]$, associated height function $\mathbb Z^2$ unbounded variance. The proof relies extension Baxter-Kelland-Wu representation multi-point correlation functions spin model. Other crucial ingredients are uniqueness and percolation properties critical random cluster measure $q\in[1,4]$, recent results relating decay correlations in delocalization function.