Duality Relations for Potts Correlation Functions

TL;DR

This paper derives duality relations for Potts model correlation functions on planar graphs, linking correlation length to surface tension and expressing three-point correlations via dual partition functions.

Contribution

It introduces new duality relations for Potts correlation functions, generalizing known results from the Ising model to arbitrary planar graphs.

Findings

Correlation length equals surface tension of the dual model.

Explicit formula for three-point correlation functions.

Duality relations hold for any planar lattice or graph.

Abstract

Duality relations are obtained for correlation functions of the q-state Potts model on any planar lattice or graph using a simple graphical analysis. For the two-point correlation we show that the correlation length is precisely the surface tension of the dual model, generalizing a result known to hold for the Ising model. For the three-point correlation an explicit expression is obtained relating the correlation function to ratios of dual partition functions under fixed boundary conditions.