Theorems on the Partition Functions of the Heisenberg Ferromagnets

Abstract

It is shown that all the zeros of the partition function lie on the unit circle in the complex `fugacity' plane and the first inequality of Griffiths, Kelly and Sherman for the spin correlation functions also holds for the anisotropic Heisenberg ferromagnets as in the Ising model. The isotropic Heisenberg ferromagnets and the Ising ferromagnets are involved as special cases and thus the methods of this article provide alternative proof of the corresponding theorems in the Ising model.