The Strong Gauss Lucas Theorem and Analyticity of Correlation Functions via the Lee-Yang Theorem

TL;DR

This paper introduces a straightforward method to derive the analyticity of correlation functions from Lee-Yang theorems, utilizing inequalities of Newman, and offers a Lee-Yang approach that bypasses complex combinatorics in low density cluster expansions for spin models.

Contribution

It presents a novel, simplified mechanism connecting Lee-Yang theorems to correlation function analyticity and introduces a combinatorics-free Lee-Yang approach for spin models.

Findings

Established a direct link between Lee-Yang theorems and correlation function analyticity.

Developed a Lee-Yang method that avoids combinatorial complexities in low density regimes.

Provided insights into the properties of spin S models using this new approach.

Abstract

We provide a simple mechanism for going from Lee-Yang type theorems to analyticity of correlation functions by exploiting under appreciated inequalities of Newman. We also describe a Lee-Yang approach that recovers the consequences of a low density cluster expansion for spin S models without any combinatorics.