The Eight-Vertex Model

M. Tanhayi-Ahari, Shahin Rouhani

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.

David A. Lavis, G. M. Bell

Yas-Hiro Quano

The eight-vertex model at the reflectionless points is considered on the basis of Smirnov's axiomatic approach. Integral formulae for form factors of the eight-vertex model can be obtained in terms of those of the eight-vertex SOS model, by using vertex-face transformation. The resulting formulae have very simple forms at the reflectionless points, and suggests us the explicit expressions of the type II vertex operators of the eight-vertex model.

Fa Yueh Wu, H. Kunz

R. J. Baxter

M J Martins

Abstract In this paper we investigate the integrability properties of a two-state vertex model on the square lattice whose microstates at a vertex always have an odd number of incoming or outcoming arrows. This model was named the odd eight-vertex model by Wu and Kunz (2004 J. Stat. Phys . 116 67) to distinguish it from the well-known eight-vertex model possessing an even number of arrow orientations at each vertex. When the energy weights are invariant under arrow inversion we show that the integrable manifold of the odd eight-vertex model coincides with that of the even eight-vertex model. The form of the -matrix for the odd eight-vertex model is however not the same as that of the respective Lax operator. Altogether we find that these eight-vertex models give rise to a generic sheaf of -matrices satisfying the Yang–Baxter equations resembling intertwiner relations associated to equidimensional representations.