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

Y. Aoun, D. Ioffe, S. Ott, Y. Velenik

Published 2021-05-08Version 1

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.