Abstract
We study the poor decay of correlations for equilibrium states of inhomogeneous fluids and solids, in the regimes of both classical and quantum statistical mechanics. Our main observation is the usefulness of the statistical mechanical expression of thestress tensor and its long-range correlations with the particle density. From this we are able to infer a very slow decay of correlations for the various molecular distribution functions under discussion. The derived results are of relevance both for completely inhomogeneous systems such as quasicrystals or granular structures and for the slightly more regular cases of, e.g., phase separating layers in fluids and solids, ideal crystals, etc. As one of the byproducts we prove the nonexistence of planequantum interfaces in two dimensions (thus extending earlier results of Requardt to the quantum regime). The results hold for arbitrary potentials of not too long range.
Similar content being viewed by others
References
J. S. Rowlinson and B. Widom,Molecular Theory of Capillarity (Oxford University Press, 1982).
J. K. Percus, Non-uniform fluids, inThe Liquid State of Matter, E. W. Montroll and J. L. Lebowitz, eds. (North-Holland, 1982).
C. A. Croxton,Statistical Mechanics of the Liquid Surface (Wiley, New York, 1980).
R. B. Griffith and D. E. Wolf, Preprint, Carnegie-Mellon University, Pittsburgh (1985).
F. P. Buff, R. A. Lovett, and F. H. Stillinger,Phys. Rev. Lett. 15:621 (1965); M.S. Wertheim,J. Chem. Phys. 65:2377 (1976); J. D. Weeks,J. Chem. Phys. 67:3106 (1977).
J. K. Percus,Faraday Symp. Chem. Soc. 16 (1981).
M. Requardt,J. Stat. Phys. 31:679 (1983).
M. Robert,Phys. Rev. Lett. 54:444 (1985).
M. Requardt,Z. Phys. B 36:187 (1979).
C. Gruber, P. A. Martin, and C. Oguey,Commun. Math. Phys. 84:55 (1982).
G. Gallavotti and E. Verboven,Nuovo Cimento 28B:274 (1975).
B. Widom and J. S. Rowlinson,J. Chem. Phys. 52:1670 (1970).
D. Ruelle,Phys. Rev. Lett. 27:1040 (1971).
J. L. Lebowitz and E. Lieb,Phys. Lett. 39A:98 (1972).
J. H. Irving and J. G. Kirkwood,J. Chem. Phys. 18:817 (1950).
P. Schofield and J. R. Henderson,Proc. R. Soc. Lond. A 379:231 (1982).
N. D. Mermin,J. Math. Phys. 8:1061 (1967).
J. G. Kirkwood and F. P. Buff,J. Chem. Phys. 17:338 (1949).
O. Bratteli and D. W. Robinson,Operator Algebras and Quantum Statistical Mechanics II, (Springer, New York, 1981).
J. Ginibre,J. Math. Phys. 6:238 (1965).
C. Gruber and P. A. Martin,Ann. Phys. 131:56 (1981).
J. G. Garrison and J. Wong,Commun. Math. Phys. 26:1 (1972).
P. A. Martin,Nuovo Cimento 68B:302 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Requardt, M., Wagner, H.J. Poor decay of correlations in inhomogeneous fluids and solids and their relevance for the physics of phase boundaries. J Stat Phys 45, 815–841 (1986). https://doi.org/10.1007/BF01020576
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01020576