The "inversion relation" method for obtaining the free energy of the chiral Potts model

TL;DR

This paper derives the free energy of the chiral Potts model using the inversion relation method, involving analyticity assumptions and symmetry considerations, and employs Wiener-Hopf factorization to relate free energy values across domains.

Contribution

It introduces a novel approach combining inversion relations, symmetry, and Wiener-Hopf factorization to compute the free energy of the chiral Potts model.

Findings

Derived the free energy using the inversion relation method.

Identified a necessary symmetry for the analytic continuation.

Connected free energy values across domains via Wiener-Hopf factorization.

Abstract

We derive the free energy of the chiral Potts model by the infinite lattice ``inversion relation'' method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that in addition to the usual assumption that the free energy be analytic and bounded in some principal domain of the rapidity parameter space that includes the physical regime, we also need a much less obvious symmetry. We can then obtain the free energy by Wiener-Hopf factorization in the complex planes of appropriate variables. Together with the inversion relation, this symmetry relates the values of the free energy in all neighbouring domains to those in the principal domain.