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Loop symmetry of integrable vertex models at roots of unity

Christian Korff, Barry M. McCoy

arXiv:hep-th/0104120Nuclear Physics BDec 1, 200116 citations

On the eight-vertex model and related models: A new method and some new results

J. Zittartz

Physica A Statistical Mechanics and its ApplicationsFeb 1, 19901 citation

Functional Equations and Fusion Matrices for the Eight Vertex Model

K. Fabricius, Barry M. McCoy

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3, 4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.

Publications of the Research Institute for Mathematical SciencesSep 30, 200435 citations

New solvable cases for the eight-vertex model

Ingo Peschel, Franz S. Rys

Physics Letters ASep 1, 198218 citations

Functional Equations and Fusion Matrices for the Eight Vertex Model

K. Fabricius, Barry M. McCoy

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3,4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.

arXiv:cond-mat/0311122Nov 6, 20030 citations

Auxiliary matrices on both sides of the equator

Christian Korff

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ -equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ -equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.

arXiv:math-ph/0408023Journal of Physics A Mathematical and GeneralDec 9, 200418 citations

New Q Matrices and Their Functional Equations for the Eight Vertex Model at Elliptic Roots of Unity

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