Inverse functional relation on the Potts model

Abstract

The two-dimensional anisotropic Potts model at all temperatures satisfies a local inverse relation leading to an inverse functional equation on the transfer matrix. The pertinence of the related functional equation for the partition function is discussed and verified perturbatively, by introducing a diagrammatic expansion corresponding to a partial resummation on one parameter of the model. Possible exploitations of the inverse relation in order to determine the partition functions are sketched. This indicates that the inverse relation can be used without referring to a star-triangle relation.