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.

arXiv comment32 pages, 6 figures, minor changes in version 2

References in corpus (5)

• Shape Fluctuations and Random Matrices
• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Partial domain wall partition functions
• Inner products of Bethe states as partial domain wall partition functions
• Exact solution of the six-vertex model with domain wall boundary conditions. Antiferroelectric phase

Cited by in corpus (7)

• The density profile of the six vertex model with domain wall boundary conditions
• Phase separation in the six-vertex model with a variety of boundary conditions
• Arctic curves of the twenty-vertex model with domain wall boundaries
• The entropy of the six-vertex model with variety of different boundary conditions
• Construction of determinants for the six-vertex model with domain wall boundary conditions
• Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition
• Boundary correlations for the six-vertex model with reflecting end boundary condition