Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Ferroelectric Phase.

This is a continuation of the paper [4] of Bleher and Fokin, 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 phase. In the present paper we obtain the large n asymptotics of Z _n in the ferroelectric phase. We prove that for any ε > 0, as n → ∞, $${Z_n\,=\,CG^nF^{n^2}[1+O(e^{-n^{1-\epsilon}})]}$$ , and we find the exact values of the constants C, G and F. The proof is based on the large n asymptotics for the underlying discrete orthogonal polynomials and on the Toda equation for the tau-function. [ABSTRACT FROM AUTHOR]