Duality and Symmetry in Chiral Potts Model

Abstract

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small $k^{\prime }$) to those of another chiral Potts model at a high temperature (of $k^{\prime -1}$). The ${\tau }^{(2)}$-model and chiral Potts model on the dual lattice are established alongside the dual chiral Potts models. With the aid of this duality relation, we exact a precise relationship between the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts model and the $s{l}_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.

Latex 34 pages, 2 figures; Typos and misprints in Journal version are corrected with minor changes in expression of some formulas

References in corpus (9)

• Transfer matrix functional relations for the generalized tau_2(t_q) model
• Derivation of the order parameter of the chiral Potts model
• The order parameter of the chiral Potts model
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• The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
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Cited by in corpus (2)

• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Spontaneous Magnetization of the Integrable Chiral Potts Model