The Conical Point in the Ferroelectric Six-Vertex Model

TL;DR

This paper investigates the low-temperature ferroelectric phase of the six-vertex model, revealing new singularities and coexistence phenomena near a unique conical point through analytical and numerical analysis.

Contribution

It provides the first detailed analysis of the ferroelectric regime, uncovering singularities and coexistence behavior at the conical point not described in earlier solutions.

Findings

Identification of a conical point with singular free energy behavior

Demonstration of multiple polarizations coexisting at the conical point

Discovery of unusual scaling properties near the conical point

Abstract

We examine the last unexplored regime of the asymmetric six-vertex model: the low-temperature phase of the so-called ferroelectric model. The original publication of the exact solution, by Sutherland, Yang, and Yang, and various derivations and reviews published afterwards, do not contain many details about this regime. We study the exact solution for this model, by numerical and analytical methods. In particular, we examine the behavior of the model in the vicinity of an unusual coexistence point that we call the ``conical'' point. This point corresponds to additional singularities in the free energy that were not discussed in the original solution. We show analytically that in this point many polarizations coexist, and that unusual scaling properties hold in its vicinity.