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Failure of Ornstein-Zernike asymptotics for the pair correlation function at high temperature and small density
Yacine Aoun1, Dmitry Ioffe2, Sébastien Ott1
1Section de Mathématiques, Université de Genève, Switzerland.
Physical Review. E
|June 17, 2021
Summary
Systems with exponentially decaying interactions may not follow Ornstein-Zernike behavior at high temperatures or low densities. This deviation is linked to the correlation length
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
Background:
- The Ornstein-Zernike approximation is a standard tool for describing correlations in physical systems.
- Understanding the limits of this approximation is crucial for accurately modeling diverse systems.
Purpose of the Study:
- To investigate the conditions under which the Ornstein-Zernike approximation fails for systems with exponentially decaying interactions.
- To explore the relationship between correlation length analyticity and asymptotic behavior.
Main Methods:
- Analysis of the pair correlation function.
- Theoretical investigation of systems with exponentially decaying potentials.
- Examination of the correlation length's behavior with temperature and density.
Main Results:
- The pair correlation function can deviate from Ornstein-Zernike asymptotics.
- This failure occurs at high temperatures and low densities.
- A lack of analyticity in the correlation length is identified as the cause, even in one-dimensional systems.
Conclusions:
- The Ornstein-Zernike approximation has limitations for systems with exponentially decaying interactions.
- Correlation length analyticity is a critical factor for asymptotic behavior.
- These findings have implications for statistical mechanics and condensed matter physics models.
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