Delocalization of the height function of the six-vertex model

We show that the height function of the six-vertex model, in the parameter range a D b D 1 and c ≥ 1, is delocalized with logarithmic variance when c ≤ 2. This complements the earlier proven localization for 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.