On the Equivalent Theory of the Generalized τ⁽²⁾-model and the Chiral Potts Model with two Alternating Vertical Rapidities

2007/10/15 by Shi-shyr Roan, Roan, Shi-shyr
Chemistry · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th #math-ph #math.AG #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.0710.2764

Latex 24 Pages; Typos and errors corrected, Confusion clarified, Improved version for clearer explanations

openalex publication_date 2007/10/15 · arxiv created 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By the Baxter's Q₇₂-operator method, we demonstrate the equivalent theory between the generalized τ⁽²⁾-model (other than two special cases with a pseudovacuum state) and the N-state chiral Potts model with two alternating vertical rapidities, where the degenerate models are included. As a consequence, the theory of the XXZ chain model associated to cyclic representations (with the parameter ς) of U_{\sf q}(sl₂) with \sf q^N=1 for odd N is identified with either (for ς^N=1) the chiral Potts model with two superintegrable vertical rapidities, or (for ς^N ≠ 1) the degenerate model for the selfdual solution of the star-triangle relation. In all these identifications, the transfer matrices T, T of the chiral Potts model (including the degenerate ones) serve as the Q_R, Q_L-operators of the corresponding τ⁽²⁾-model, so that the functional relations hold as in the solvable N-state chiral Potts model.

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