It is shown that the disorder solutions exhibited by two-dimensional statistical lattice systems verify the star-triangle relation. These solutions of the star-triangle relation are of a different type than those corresponding to completely integrable models.
The study of the two-dimensional models in lattice statistics and the related exactly integrable 1+1 dimensional field theory has developed intensively over the past ten years and this evolution, this developement does not seem to decrease. There are several reasons why one can be interested in such models: the need to leave the framework of perturbation theory with the hope to describe particle spectrum and scattering, the fact that some 1+1 dimensional exactly solved models have physical applications for some important solid state theories (Solitons in magnets [61,11], Peierls-Frohlich model, Anderson localization, Kondo effects [19,37,1]),the importance of exactly solved two-dimensional models of lattice statistics to understand the critical phenomena (universality...). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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).