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

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

2006-11-13

arxiv.org/abs/cond-mat/0611316v4

J.Phys.A40:11019-11044,2007

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1751-8113/40/36/004

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 $\eta = \frac{2m K}{N}$ 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.

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