We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal formula for the partition function, its reduction to orthogonal polynomials, and on an asymptotic analysis of the orthogonal polynomials under consideration in the framework of the Riemann--Hilbert approach.
Comment: 19 pages, 3 figures. Results are now stated for domain wall boundary conditions with rotational symmetry rather than for half-turn boundary conditions as in an earlier version. Accordingly the title is changed slightly, but the technical content is unchanged in v2