# Domain wall six-vertex model with half-turn symmetry

## TL;DR

This paper derives asymptotic formulas for the partition function of a symmetric six-vertex model with domain wall boundary conditions, using advanced mathematical techniques involving orthogonal polynomials and Riemann-Hilbert analysis.

## Contribution

It introduces a novel asymptotic analysis of the partition function for the half-turn symmetric six-vertex model across different phase regions.

## Key findings

- Asymptotic formulas for the partition function in each phase region
- Application of Riemann-Hilbert method to orthogonal polynomial analysis
- Extension of determinantal formula techniques to symmetric boundary conditions

## Abstract

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal formula for the partition function, its reduction to orthogonal polynomials, and on an asymptotic analysis of the orthogonal polynomials under consideration in the framework of the Riemann--Hilbert approach.