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arXiv:solv-int/9903001 · Journal of Physics A Mathematical and General

Functional relations and nested Bethe ansatz forsl(3) chiral Potts model at

Herman E. Boos, Vladimir V. Mangazeev

Published Jan 1, 1999• 6 citations
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Abstract

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl (3) chiral Potts model for . For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.

DOI
10.1088/0305-4470/32/16/012

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All eigenvalues of the transfer matrix of the integrable 3-state Potts model are computed as polynomials in the spectral variable for chains of length M ≤7. The zeroes of the eigenvalues are known to satisfy a Bethe's Ansatz equation and thus it is of particular interest that we find many solutions whose zeroes do not satisfy the traditional "string hypothesis". We also find many cases where the integers in the logarithmic form of the Bethe equations do not satisfy the monotonicity properties that they are usually assumed to possess. We present a classification of all eigenvalues in terms of sets of roots and show that, for all M, this classification yields a complete set.