The Potts model and flows: I. The pair correlation function

It is shown that the partition function for the A-state Potts model with pair interactions is related to the expected number of integer mod-A flows in a percolation model. The relation is generalised to the pair correlation function. The resulting high- temperature expansion coefficients are shown to be the flow polynomials of graph theory. We also prove an observation of Tsallis and Levy concerning the equivalent transmissivity of a cluster.