Duality and Symmetry in Chiral Potts Model

Details Duality and Symmetry in Chiral Potts Model Duality and Symmetry in Chiral Potts Model

2009-05-12

arxiv.org/abs/0905.1924v5

J.Stat.Mech.0908:P08012,2009

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1742-5468/2009/08/P08012

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 $k'$) to those of another chiral Potts model at a high temperature (of $k'^{-1}$). 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 $sl_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.

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