zbMATH — the first resource for mathematics

Generalized generalized spin models associated with exactly solvable models. (English) Zbl 0854.05102
Bannai, E. (ed.) et al., Progress in algebraic combinatorics. Based on the international symposium on algebraic combinatorics, Fukuoka, Japan, 1993 and the research project on algebraic combinatorics, Kyoto, Japan, April 1994 – March 1995. Kyoto: Kinokuniya Company Ltd. Adv. Stud. Pure Math. 24, 81-100 (1996).
Summary: We show a close connection between generalized generalized spin models (four-weight spin models) and exactly solvable models. The defining relations of four-weight spin models are discussed from the viewpoint of the star-triangle relations. For an illustration we derive symmetric spin models from the self-dual \(Z_N\) model, and then construct various four-weight spin models through gauge transformations. We also show that the gauge transformations do not change the values of the link invariants derived from the four-weight spin models.
For the entire collection see [Zbl 0845.00006].

05E30 Association schemes, strongly regular graphs