Generalized Generalized Spin Models Associated with Exactly Solvable Models

Abstract

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.