2009/04/30 by Pavel Bleher, Karl Liechty
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-008-0709-9
69 pages, 10 figures
arxiv created 2009/12/16 · arxiv updated 2010/01/07
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=\sinh(\ga-t), b=\sinh(\ga+t), c=\sinh(2\ga), |t|<\ga. We prove the conjecture of Zinn-Justin, that as n→∞, Zn=Cþ4(n\om) Fn2[1+O(n-1)], where \om and F are given by explicit expressions in \ga 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.