XYZ and eight-vertex models

Yu. G. Stroganov

David A. Lavis, G. M. Bell

Barry M. McCoy

Abstract This chapter derives the matrix TQ functional equation for the eight-vertex model. The Bethe's equation for the eigenvalues of Q is derived from the matrix TQ equation. A numerical study is made of the eigenvalues of Q, and the TQ equation is used to compute the free energy of the eight-vertex model. Results on the excitations, order parameters and correlation functions of the six- and eight-vertex models and the related XYZ spin chain are presented.

Christian Hagendorf, Paul Fendley

We show that the XYZ spin chain along the special line of couplings J x J y +J x J z +J y J z =0 possesses a hidden $\\mathcal{N}=(2,2)$ supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer matrix of the corresponding eight-vertex model. In particular, it is shown how to derive the supercharges from Baxter's Bethe ansatz. This analysis leads to new conjectures concerning the ground state for chains of odd length. We also discuss a correspondence between the spectrum of this XYZ chain and that of a manifestly supersymmetric staggered fermion chain

R. J. Baxter

David A. Lavis, G. M. Bell