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

TL;DR

This paper derives an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase, using discrete orthogonal polynomials and determinant analysis.

Contribution

It introduces a novel asymptotic analysis method for the partition function involving discrete orthogonal polynomials and determinant formulas in the ferroelectric phase.

Findings

Derived an explicit asymptotic formula for the partition function.

Connected the determinant representation to Meixner polynomials.

Provided insights into the ferroelectric phase behavior.

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.