Duality in two-dimensional Z(N)-symmetric spin models on a finite lattice

Abstract

We propose a method for deriving duality relations for two-dimensional inhomogeneous Z(N)-symmetric models on a finite square lattice wound around a torus. The method is used to obtain duality relations for the vector Potts model, the Berezinskii-Villain Z(N)-model, the Ashkin-Teller model, and the 8-vertex model on a lattice obliquely wound around a torus, as well as an exact relation linking the partition functions of the latter two models.