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

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.

32 pages, 6 figures, minor changes in version 2

References in corpus (1)

• Partial domain wall partition functions

Cited by in corpus (1)

• The entropy of the six-vertex model with variety of different boundary conditions