Self-dual property of the Potts model in one dimension
  A new duality relation is derived for the Potts model in one dimension. It is shown that the partition function is self-dual with the nearest-neighbor interaction and the external field appearing as dual parameters. Zeroes of the partition function are analyzed. Particularly, we show that the new duality relation implies a circle theorem in the complex temperature plane for the one-dimensional Ising model. 
F. Y. Wu (Northeastern University)