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Journal de Physique I

La relation étoile-triangle d'un modèle elliptique ZN

M. Gaudin

Published Mar 1, 1991• 10 citations
Publisher

Abstract

We give a proof of the star-triangle relation for an elliptic generalisation of the Fateev and Zamolodchikov model with symmetry ZN.
DOI
10.1051/jp1:1991137

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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).

Journal of Physics A Mathematical and General•Apr 21, 1984•5 citations
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).