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arXiv · 1407.8483

Six-vertex model with partial domain wall boundary conditions: ferroelectric phase

Pavel Bleher·Karl Liechty
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Abstract

We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the determinant of a matrix of mixed Vandermonde/Hankel type. This determinant can be expressed in terms of a system of discrete orthogonal polynomials, which can then be evaluated asymptotically by comparison with the Meixner polynomials.

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Pavel Bleher, Karl Liechty. 2015-02-20. Six-vertex model with partial domain wall boundary conditions: ferroelectric phase. https://doi.org/10.1063/1.4908227

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