Related Models

Sei Suzuki, Jun‐ichi Inoue, Bikas K. Chakrabarti

J.-M. Maillard, Thomas Garel

For pt.I see ibid, vol.17, p.1251 (1984). The authors continue their study of the star-triangle relation for two-component spin models, with the help of the inversion relation. The conclusion is that the most general interaction-round-a-face models (16 non-zero parameters) that satisfy the star-triangle relations are mainly Baxter (1972) and Fan and Wu (1970) models. In this way they recover Krichever's result (1981) for the classification of the star-triangle relations for vertex models. They sketch a generalisation of this approach to models with excluded configurations, to staggered models, and to three-dimensional models (tetrahedron relations).

Stefan Flörchinger

Masao Nomura

A trigonometric function parametrization of Yang-Baxter (Y-B) relations is described in terms of n - j symbols of su q (2), a deformation of su (2). The formalism starts with deduction of the Y-B relation for the IRF (interaction round a face) model of su q (2) from a general operator relation for the vertex model. The relation obtained for the IRF model is transformed into the Y-B relation for the vertex model using the property that the 3- j symbol is an asymptotic limit of the 6- j symbol. A class of very general solutions to Y-B equations is also presented. This solution of the IRF model with infinite rapidity parameters is linked to a symmetry of the 12- j symbol of the second kind.

Ian Graham Enting

It is pointed out that the eight-vertex model, the triplet model and the Ashkin-Teller (1943) model have a common exponent relation beta e = 1 / 4 - 1 / 4 alpha that is not a consequence of scaling theory. It is proposed that this relation reflects a special symmetry of these models and this proposal is related to possible classification of two-dimensional systems.