Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large $n$ asymptotics of $Z_n$ on the critical line between these two phases.