 05389 Pavel M. Bleher and Vladimir V. Fokin
 Exact Solution of the SixVertex Model with Domain Wall Boundary Conditions. Disordered Phase
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Nov 13, 05

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Abstract. The sixvertex model, or the square ice model, with domain wall boundary conditions (DWBC)
has been introduced and solved for finite $N$ by Korepin and Izergin. The solution is based on
the YangBaxter equations and it represents the free energy in terms of an $N\times N$ Hankel
determinant. Paul ZinnJustin observed that the IzerginKorepin formula can be reexpressed
in terms of the partition function of a random matrix model with a nonpolynomial interaction.
We use this observation to obtain the large $N$ asymptotics of the sixvertex model with DWBC
in the disordered phase.
The solution is based on the RiemannHilbert approach and the DeiftZhou nonlinear steepest
descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign
matrices (the ASM problem) is a special case of the the sixvertex model. We compare the
obtained exact solution of the sixvertex model with known exact results for the
1, 2, and 3 enumerations of ASMs, and also with the exact solution on the socalled free
fermion line.
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