Some Applications of the Lee-Yang Theorem

TL;DR

This paper provides a simple proof of the analyticity of correlations in lattice statistical mechanics models with the Lee-Yang property, and surveys models with this property and their applications.

Contribution

It offers a straightforward proof of correlation analyticity and reviews models with the Lee-Yang property and their applications.

Findings

Correlations are analytic in the external magnetic field for models with Lee-Yang property.

Survey of models known to satisfy the Lee-Yang circle theorem.

Applications of analyticity in magnetic field are discussed.

Abstract

For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.