The Lee-Yang property of isotropic vector ferromagnets and lattice fields

Abstract

The Lee-Yang property of a given spin model means that its partition function has purely imaginary zeros as a function of an external magnetic field. A similar property is also used in the theory of quantum anharmonic crystals and quantum lattice fields. A number of powerful analytic methods of the mathematical theory of such models employ this property. Its suitable generalization is used in the theory of models of isotropic $D$-dimensional spins (rotors) or $D$-component quantum lattice fields. So far, the (generalized) Lee-Yang property has been established only for two-dimensional isotropic models. In this work, we prove that isotropic spin and field models living on $\mathds{Z}$ have this property for all even $D$.