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. 

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References

SHOWING 1-10 OF 20 REFERENCES
Ornstein-Zernike theory for finite range Ising models above Tc
Abstract. We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈Σ0Σx〉β in the general context of finite range Ising type models on ℤd. The proof relies in
Rigorous nonperturbative Ornstein-Zernike theory for Ising ferromagnets
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical.
Non-analyticity of the Correlation Length in Systems with Exponentially Decaying Interactions
We consider a variety of lattice spin systems (including Ising, Potts and XY models) on Z^d with long-range interactions of the form J_x = psi(x) exp(-|x|), where psi(x) = exp(o(|x|)) and |·| is an
Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field
We prove that the correction to exponential decay of the truncated two points function in the homogeneous positive field Ising model is $$c\Vert x\Vert ^{-(d-1)/2}$$ c ‖ x ‖ - ( d - 1 ) / 2 . The
The phase transition in a general class of Ising-type models is sharp
For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ϕ4 models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic
Correlation Functions and the Critical Region of Simple Fluids
The ``classical'' (e.g. van der Waals) theories of the gas‐liquid critical point are reviewed briefly and the predictions concerning the nature of the singularities of the coexistence curve, the
Condensation for random variables conditioned by the value of their sum
  • C. Godrèche
  • Mathematics
    Journal of Statistical Mechanics: Theory and Experiment
  • 2019
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a
Interface, Surface Tension and Reentrant Pinning Transition in the 2d Ising Model
We develop a new way to look at the high-temperature representation of the Ising model up to the critical temperature and obtain a number of interesting consequences. In the two-dimensional case, it
Interface, Surface Tension and Reentrant Pinning Transition in the 2D Ising Model
Abstract: We develop a new way to look at the high-temperature representation of the Ising model up to the critical temperature and obtain a number of interesting consequences. In the two-dimensional
Existence of the critical point in φ4 field theory
We consider the φ4 quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m(σ) decreases continuously to zero as the bare
...
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