Geodesic
Power and exponential asymptotic forms of correlation functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 454-464

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Using the Ornstein–Zernike equation, we obtain two asymptotic equations, one describing the exponential asymptotic behavior and the other describing the power asymptotic behavior of the total correlation function $h(r)$. We show that the exponential asymptotic form is applicable only on a bounded distance interval $l. The power asymptotic form is always applicable for $r>L$ and reproduces the form of the interaction potential. In this case, as the density of a rarified gas decreases, $L\to l$, the exponential asymptotic form vanishes, and only the power asymptotic form remains. Conversely, as the critical point is approached, $L\to\infty$, and the applicability domain of the exponential asymptotic form increases without bound.
Keywords: asymptotic form, correlation function, Ornstein–Zernike equation. 
G. A. Martynov. Power and exponential asymptotic forms of correlation functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 454-464. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a9/
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     title = {Power and exponential asymptotic forms of correlation functions},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a9/}
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