Abstract
The Gibbsian N-body density function of a Hamiltonian H N that is rotationally and translationally invariant must itself be rotationally and translationally invariant, as must then also be all reduced n-body density functions of this Hamiltonian. In particular, the one-body density is a constant and the two-body density depends only on relative coordinates. An external field destroys this homogeneity, producing anisotropy or nonuniformity [1, 2], and so makes necessary the joint calculation of the coupled one-body and two-body density functions. A striking if familiar example of the response of a bulk system to an external field is ferromagnetism. We shall use this particular case here to present a general procedure to compute the coupled one-body and two-body density functions of an inhomogeneous classical fluid in an external field. Remarkably, the procedure is no more difficult to carry through than similar calculations for ordinary homogeneous systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
N.D. Mermin, Phys. Rev. A 137, 1441 (1965).
J.R. Henderson, in Fundamentals of Inhomogeneous Fluids (Dekker, New York, 1992), edited by D. Henderson, Chap. 2.
J. S. Høye and G. Stell, Phys. Rev. Lett. 36, 1569 (1976).
M. J. P. Nijmeijer and J. J. Weis, Phys. Rev. Lett. 75, 2887 (1995)
M. J. P. Nijmeijer and J. J. Weis, Phys. Rev. E 53, 591 (1996).
J. J. Weis, M. J. P. Nijmeijer, J. M. Tavares, and M. M. Telo da Gama, Phys. Rev. E 55, 436 (1997).
E. Lomba, J. J. Weis, N. G. Aimarza, F. Bresme, and G. Stell, Phys. Rev. E 49, 5169 (1994).
J. M. Tavares, M. M. Telo da Gama, P. I. C. Teixeira, J. J. Weis, and M. J. P. Nijmeijer, Phys. Rev. E 52, 1915 (1995).
See G. S. Cargill II and R. W. Cochrane, in Amorphous Magnetism, edited by H. O. Hooper and A. M. de Graaf (Plenum, New York, 1973), p. 313.
G. Bush and H. J. Guentherodt, Phys. Lett. 27A, 110 (1968)
B. Kraeft and H. Alexander, Phys. Konden. Mater. 16, 281 (1973).
T. Albrecht, C. Bührer, M. Fähnie, K. Maier, D. Platzek, and J. Reske, Appl. Phys. A 65, 215 (1997).
J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, London, 1986).
D. Henderson, in Fundamentals of Inhomogeneous Fluids (Dekker, New York, 1992), edited by D. Henderson, Chap. 4.
F. Lado and E. Lomba, Phys. Rev. Lett. 80, 3535 (1998).
F. Lado, E. Lomba, and J. J. Weis, Phys. Rev. E (to be published).
F. Lado, Phys. Rev. E 55, 426 (1997).
C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids (Clarendon, Oxford, 1984), Volume 1.
See, for example, G. Arfken, Mathematical Methods for Physicists (Academic, Orlando, 1985), Chap. 9.
N. I. Akhiezer, The Classical Moment Problem (Hafner, New York, 1965), Chap. 1.
F. Lado, Mol. Phys. 47, 283 (1982).
Since the interatomic vector r 12 is completely decoupled from the spin orientations ŝ1 and ŝ2 in the Heisenberg fluid, the solution of the (OZ + closure) equations here is actually simpler than that described in Ref. [19).
G. Zerah and J. P. Hansen, J. Chem. Phys. 84, 2336 (1986).
L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, (Pergamon, Oxford, 1984), Second Edition, Section 46.
C. Holm and W. Janke, Phys. Rev. B 48, 936 (1993).
K. Chen, A. M. Ferrenberg, and D. P. Landau, Phys. Rev. B 48, 3249 (1993).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lado, F., Lomba, E. (1999). Inhomogeneous Fluids in an External Field. In: Caccamo, C., Hansen, JP., Stell, G. (eds) New Approaches to Problems in Liquid State Theory. NATO Science Series, vol 529. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4564-0_14
Download citation
DOI: https://doi.org/10.1007/978-94-011-4564-0_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5671-4
Online ISBN: 978-94-011-4564-0
eBook Packages: Springer Book Archive