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

الأصل · EN

We obtain the large n asymptotics of the partition function Zₙ of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights a=(-t), b=(+t), c=(2), |t|<. We prove the conjecture of Zinn-Justin, that as n→∞, Zₙ=Cþ₄(n) Fⁿ²[1+O(n⁻¹)], where and F are given by explicit expressions in and t, and þ₄(z) is the Jacobi theta function. The proof is based on the Riemann-Hilbert approach to the large n asymptotic expansion of the underlying discrete orthogonal polynomials and on the Deift-Zhou nonlinear steepest descent method.