Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases

TL;DR

This paper derives the exact large $n$ asymptotics of the partition function for the six-vertex model with domain wall boundary conditions specifically on the critical line separating ferroelectric and disordered phases.

Contribution

It provides the first exact asymptotic analysis of the partition function on the critical phase boundary, extending previous results for other phases.

Findings

Large $n$ asymptotics of $Z_n$ on the critical line obtained

Bridges the gap between disordered and ferroelectric phase analyses

Enhances understanding of phase transition behavior in the six-vertex model

Abstract

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large $n$ asymptotics of $Z_n$ on the critical line between these two phases.