FUSION OF A-D-E LATTICE MODELS

Abstract

Fusion hierarchies of A-D-E face models are constructed. The fused critical D, E and elliptic D models yield new solutions of the Yang-Baxter equations with bond variables on the edges of faces in addition to the spin variables on the corners. It is shown directly that the row transfer matrices of the fused models satisfy special functional equations. Intertwiners between the fused A-D-E models are constructed by fusing the cells that intertwine the elementary face weights. As an example, we calculate explicitly the fused 2×2 face weights of the 3-state Potts model associated with the D4 diagram as well as the fused intertwiner cells for the A5-D4 intertwiner. Remarkably, this 2×2 fusion yields the face weights of both the Ising model and 3-state CSOS models.