Pavel M. Bleher and Vladimir V. Fokin
Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
(755K, Postscript)

ABSTRACT.  The six-vertex 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 Yang-Baxter equations and it represents the free energy in terms of an $N\times N$ Hankel 
determinant. Paul Zinn-Justin observed that the Izergin-Korepin formula can be re-expressed 
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 six-vertex model with DWBC 
in the disordered phase. 
The solution is based on the Riemann-Hilbert approach and the Deift-Zhou 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 six-vertex model. We compare the 
obtained exact solution of the six-vertex model with known exact results for the 
1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called free 
fermion line.