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

Yacine Aoun; Dmitry Ioffe; Sébastien Ott; Yvan Velenik

doi:10.1103/PhysRevE.103.L050104

Letter

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

Yacine Aoun^1,*, Dmitry Ioffe², Sébastien Ott ^1,†, and Yvan Velenik ^1,‡

¹Section de Mathématiques, Université de Genève, Switzerland
²Faculty of Industrial Engineering and Management, Technion Israel Institute of Technology, Technion City, Israel

^*Yacine.Aoun@unige.ch
^†ott.sebast@gmail.com
^‡Yvan.Velenik@unige.ch

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Phys. Rev. E 103, L050104 – Published 26 May, 2021

DOI: https://doi.org/10.1103/PhysRevE.103.L050104

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.

Physical Review E

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

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

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