Abstract

Failure of Ornstein-Zernike asymptotics for the pair correlation function at high temperature and small density Y. Aoun, D. Ioffe, S. Ott, Y. Velenik Physical Review E 103, L050104 (2021). 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. Key words: Ising model, Potts model, XY model, random cluster model, Ornstein-Zernike asymptotics, correlation length, analyticity Files: PDF file, Published version, bibtex, slides, talk