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=b=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.