Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions: Antiferroelectric Phase
نویسندگان
چکیده
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 D sinh. t/, b D sinh. C t/, c D sinh.2 /, jt j < . We prove the conjecture of Zinn-Justin, that as n ! 1, Zn D C#4.n!/F n Œ1 C O.n 1/ , where ! and F are given by explicit expressions in and t , and #4. ́/ 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 steepestdescent method. © 2009 Wiley Periodicals, Inc.
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Six-vertex model with domain wall boundary conditions and one-matrix model
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