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

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dc.creatorRoan, Shi-shyr
dc.date2007-10-15
dc.date2008-02-12
dc.date.accessioned2026-07-07T09:19:43Z
dc.date.available2026-07-07T09:19:43Z
dc.descriptionBy the Baxter's $Q_{72}$-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 $U_{\sf q}(sl_2)$ 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 $ς^N \neq 1$) the degenerate model for the selfdual solution of the star-triangle relation. In all these identifications, the transfer matrices $T, \hat{T}$ 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.
dc.descriptionLatex 24 Pages; Typos and errors corrected, Confusion clarified, Improved version for clearer explanations
dc.identifierhttps://arxiv.org/abs/0710.2764
dc.identifierhttp://arxiv.org/abs/0710.2764
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154493
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn the Equivalent Theory of the Generalized τ^{(2)}-model and the Chiral Potts Model with two Alternating Vertical Rapidities
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