On the duality relation for correlation functions of the Potts model

TL;DR

This paper proves a conjecture on the duality relation for correlation functions in the Potts model, providing explicit formulas and sum rule identities, with extensions to chiral and multi-component variants.

Contribution

It establishes the explicit duality relation for n-site correlation functions of the Potts model and extends the results to chiral and multi-component models.

Findings

Derived explicit duality expressions for correlation functions.

Established sum rule identities via M"obius inversion.

Extended duality results to chiral and multi-component Potts models.

Abstract

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.