The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N

Abstract

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta =\frac{2mK}{N}$ with odd $N$ where Q_{72} 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 SOS model.

Latex 28 page; Typos corrected, minor changes in presentation, References added and updated-Journal version

References in corpus (3)

• Analytic theory of the eight-vertex model
• An elliptic current operator for the 8 vertex model
• Root of unity symmetries in the 8 and 6 vertex models

Cited by in corpus (4)

• The TQ equation of the 8 vertex model for complex elliptic roots of unity
• New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
• On $Q$-operators of XXZ Spin Chain of Higher Spin
• Bethe Equation of ${\tau }^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities