On the duality relation for correlation functions of the Potts model

Details On the duality relation for correlation functions of the Potts model On the duality relation for correlation functions of the Potts model

1997-12-03

arxiv.org/abs/cond-mat/9712045v3

J. Phys. A, 31(1998) 2823-2836

Physics

Condensed Matter

Statistical Mechanics

17 pages in RevTex, 5 figures, submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/31/12/008

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.

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