Exact solution of the six-vertex model with domain wall boundary conditions. Ferroelectric phase

摘要

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,=,CGnF{n2}[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.