The Q-operator and functional relations of the eight-vertex model at root-of-unity for odd N

Abstract

Following Baxter's method of producing Q72-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter with odd N where Q72 does not exist. We use this new Q-operator to study the functional relations in the Fabricius–McCoy comparison between the root-of-unity eight-vertex model and the superintegrable N-state chiral Potts model. By the compatibility of the constructed Q-operator with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we verify the set of functional relations of the root-of-unity eight-vertex model using the explicit form of the Q-operator and fusion weights of the SOS model.