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

TL;DR

This paper proves that isotropic spin and field models on the integer lattice have the Lee-Yang property for all even dimensions, extending previous results limited to two dimensions.

Contribution

It generalizes the Lee-Yang property to isotropic models on Z for all even dimensions, broadening the scope of models with this property.

Findings

Established the Lee-Yang property for models on Z in all even dimensions.

Extended the known two-dimensional results to higher even dimensions.

Provided new analytic tools for quantum lattice field theories.

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 $D$.