The six-vertex model, or the square ice model, with domain wall bound- ary conditions (DWBC) has been introduced and solved for finiteN by Korepin and Izergin. The solution is based on theYang-Baxter equations and it represents the free energy in terms of an N × 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 observa- tion to obtain the large N asymptotics of the six-vertex model with DWBC in the disordered phase and ferroelectric phases, and also on the critical line between these two phases. The solution is based on the Riemann-Hilbert approach.
CITATION STYLE
Bleher, P. M. (2009). Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. In New Trends in Mathematical Physics (pp. 59–72). Springer Netherlands. https://doi.org/10.1007/978-90-481-2810-5_5
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