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

@article{Aoun2021FailureOO, title={Failure of Ornstein-Zernike asymptotics for the pair correlation function at high temperature and small density.}, author={Yacine Aoun and Dmitry Ioffe and S{\'e}bastien Ott and Yvan Velenik}, journal={Physical review. E}, year={2021}, volume={103 5}, pages={ L050104 } }

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.

## 2 Citations

Ornstein-Zernike behavior for Ising models with infinite-range interactions

- Mathematics
- 2021

We prove Ornstein–Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the…

On the two-point function of the Potts model in the saturation regime

- Mathematics
- 2022

. We consider FK percolation on Z d with interactions of inﬁnite range of the form J x = ψ ( x ) e − ρ ( x ) with ρ a norm on Z d and ψ a subexponential correction. We ﬁrst provide an optimal…

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