Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases

Abstract

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, 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 and ferroelectric phases, respectively. In the present paper we obtain the large $n$ asymptotics of $Z_n$ on the critical line between these two phases.

22 pages, 6 figures, to appear in the Journal of Statistical Physics

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• A numerical study of the F-model with domain-wall boundaries
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• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis
• Thermodynamic limit of the six-vertex model with reflecting end
• The entropy of the six-vertex model with variety of different boundary conditions
• Emptiness formation probability of the six-vertex model and the sixth Painlevé equation
• On the thermodynamic limit of the 6-vertex model
• Boundary correlations for the six-vertex model with reflecting end boundary condition
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Exact solution of the six-vertex model with domain wall boundary conditions. Critical line between disordered and antiferroelectric phases