Discrete Holomorphic Parafermions in the Eight Vertex Model

TL;DR

This paper demonstrates the existence of holomorphic Parafermions in the eight vertex model, extending concepts from the six vertex model and linking to the Ashkin-Teller and O(n) models at critical points.

Contribution

It extends the definition of holomorphic Parafermions from the six vertex to the eight vertex model, revealing their presence on the critical plane and in integrable cases.

Findings

Parafermions exist in the eight vertex model on the critical plane.

Connection established between the eight vertex and Ashkin-Teller models.

Link between the eight vertex model and the O(n) model confirmed.

Abstract

We show that holomorphic Parafermions exist in the eight vertex model. This is done by extending the definition from the six vertex model to the eight vertex model utilizing a parameter redefinition. These Parafermions exist on the critical plane and integrable cases of the eight vertex model. We show that for the case of staggered eight vertex model, these Parafermions correspond to those of the Ashkin-Teller model. Furthermore, the loop representation of the eight vertex model enabled us to show a connection with the O(n) model which is in agreement with the six vertex limit found as a special case of the O(n) model.