Failure of Ornstein--Zernike asymptotics for the pair correlation function at high temperature and small density

TL;DR

This paper demonstrates that the Ornstein-Zernike asymptotic behavior of the pair correlation function can fail at high temperatures and low densities due to non-analyticity in the correlation length, even in one-dimensional systems.

Contribution

It reveals conditions under which Ornstein-Zernike asymptotics break down, highlighting the role of analyticity in correlation functions at high temperature and low density.

Findings

Ornstein-Zernike asymptotics can fail at high temperature and small density.

Failure linked to non-analyticity of the correlation length.

Occurs even in one-dimensional systems.

Abstract

We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all sufficiently high temperatures and all sufficiently small densities. This turns out to be related to a lack of analyticity of the correlation length as a function of temperature and/or density and even occurs for one-dimensional systems.