Equations for Correlation Functions of Eight-Vertex Model: Ferromagnetic and Disordered Phases

TL;DR

This paper extends analytical methods for calculating correlation functions in the eight-vertex model from antiferromagnetic to ferromagnetic and disordered phases, utilizing Baxter's symmetries for parametrization and phase relation insights.

Contribution

It introduces a novel extension of existing analytical techniques to new phases of the eight-vertex model using Baxter's symmetries.

Findings

Derived equations for correlation functions in ferromagnetic phase

Established relations between phases via symmetry considerations

Validated analytical approach for disordered phase

Abstract

The Kyoto group (Jimbo, Miwa, Nakayashikiet al.) showed that the partition function and correlation funtions of the eight-vertex model in antiferromagnetic phases can be calculated using simple analytical properties of the $R$-matrix. We extend these methods to ferromagnetic and disordered phases. We use Baxter's symmetries to obtain appropriate parametrizations of the $R$-matrix and to substantiate the validity of the analytical approach for these phases. These symmetries allow one to relate correlation functions in different phases.