Difference equations for the correlation functions of the eight vertex model

TL;DR

This paper derives difference equations governing correlation functions of the eight vertex model, solving a key equation to confirm a conjectured polarization and exploring related vertex operator constructions.

Contribution

It introduces difference equations for inhomogeneous eight vertex model correlations and confirms a conjecture on spontaneous polarization.

Findings

Derived difference equations for correlation functions.

Solved the simplest equation to confirm the polarization conjecture.

Discussed vertex operator constructions on the lattice.

Abstract

We propose that the correlation functions of the inhomogeneous eight vertex model in the anti-ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters. Solving the simplest difference equation we obtain the expression for the spontaneous staggered polarization conjectured by Baxter and Kelland. We discuss also a related construction of vertex operators on the lattice.