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.
@article{TMF_2008_156_3_a9,
author = {G. A. Martynov},
title = {Power and exponential asymptotic forms of correlation functions},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {454--464},
publisher = {mathdoc},
volume = {156},
number = {3},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a9/}
}
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/