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

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Abstract

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.

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Correspondence to Pavel Bleher.

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Communicated by H. Spohn

The first author is supported in part by the National Science Foundation (NSF) Grant DMS-0652005.

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Bleher, P., Liechty, K. Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Ferroelectric Phase. Commun. Math. Phys. 286, 777–801 (2009). https://doi.org/10.1007/s00220-008-0709-9

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