Abstract
We study the decay of correlation of the two-particle distribution function in a plane phase separating layer (e.g., a liquid in coexistence with its vapor). We argue that the decay may be poorer in this special case than in the more general situation of interfaces of arbitrary shape. The clustering is shown to be weaker than ¦x − y¦ − (d − 2), d the space dimension, in contrast to the more general situation. In particular, we show that this poor clustering is entirely restricted to the interface itself. This stronger result allows to prove as a by-product the nonexistence of a plane interface in two dimensions. Furthermore we make some remarks concerning the physical consequences like, e.g., the degree of particle number fluctuations and the behavior of the compressibility in the interface. The results do hold for two-particle potentials of short range.
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References
P. A. Eglestaff,An Introduction to the Liquid State (Academic Press, New York, 1967).
H. L. Frisch and J. L. Lebowitz,The Equilibrium Theory of Classical Fluids (Benjamin, New York, 1964).
N. D. Mermin,Phys. Rev. 176:250 (1968).
J. Fröhlich and Ch. E. Pfister,Commun. Math. Phys. 81:277 (1981).
M. Requardt,Z. Phys. B 36:187 (1979).
Ch. Gruber, Ph. A. Martin, and Ch. Oguey,Commun. Math. Phys. 84:55 (1982).
Ch. Gruber, and Ph. A. Martin,Phys. Rev. Lett. 45:853 (1980).
M. Requardt, preprint, Göttingen, 1982.
M. Requardt,J. Stat. Phys. 29:119 (1982).
Ph. A. Martin,Nuov. Ciment. B 68:303 (1982).
M. S. Wertheim,J. Chem. Phys. 65:2377 (1976).
L. Landau, J. Fernando Perez, and W. F. Wreszinski, to appearJ. Stat. Phys., 1982.
H. Reeh,Fortschr. Phys. 16:687 (1968).
M. Requardt,Commun. Math. Phys. 50:259 (1976).
C. A. Croxton,Liquid State Physics (Cambridge University Press, Cambridge, 1974).
H. Narnhofer, Wien preprint, 1982, to appearJ. Stat. Phys.
D. Ruelle,Phys. Rev. Lett. 27:1040 (1971); J. L. Lebowitz and E. H. Lieb,Phys. Lett. 39A:98 (1972).
C. Croxton,Statistical Mechanics of the Liquid Surface (Wiley, New York, 1980).
J. K. Percus, Non-uniform fluids, inStudies in Stat. Mech., Vol. VIII, E. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1982).
J. Bricmont, J. L. Lebowtiz, and C. E. Pfister,J. Stat. Phys. 26:313 (1981).
J. Fröhlich, C. E. Pfister, and T. Spencer, IHES preprint, 1982.
B. Widom, inPhase Transfer and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, New York, 1972).
D. Ruelle,Statistical Mechanics Rigorous Results (Benjamin, New York, 1969).
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Requardt, M. The decay of correlation of the two-particle distribution function in a phase-separating layer and the possibility of spatial phase coexistence. J Stat Phys 31, 679–689 (1983). https://doi.org/10.1007/BF01019505
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DOI: https://doi.org/10.1007/BF01019505