Abstract
A thermodynamic system of equally charged, plus and minus, classical particles constrained to move in a (spherical) ball is studied in a region of parameters in which Debye screening takes place. The activities of the two charge species are not taken as necessarily equal. We must deal with two physically interesting surface effects, the formation of a surface charge layer, and long range forces reaching around the outside of the spherical volume. This is an example in as much as 1) general charge species are not considered, 2) the volume is taken as a ball, 3) a simple choice for the short range forces (necessary for stability) is taken. We feel the present system is general enough to exhibit all the interesting physical phenomena, and that the methods used are capable of extension to much more general systems. The techniques herein involve use of the sine-Gordon transformation to get a continuum field problem which in turn is studied via a multi-phase cluster expansion. This route follows other recent rigorous treatments of Debye screening.
Similar content being viewed by others
References
Battle, G.A.: A new combinatoric estimate for cluster expansions. Commun. Math. Phys.94, 133–139 (1984)
Battle, G.A., Federbush, P.: A phase cell cluster expansion for Euclidean field theories. Ann. Phys.142, 95–139 (1982)
Battle, G.A., Federbush, P.: A note on cluster expansions, tree graph identities, extra 1/N! factors!!!, Lett. Math. Phys.8, 55–57 (1984)
Brydges, D.: A rigorous approach to Debye screening in dilute classical Coulomb systems. Commun. Math. Phys.58, 313–350 (1978)
Brydges, D.: A short course on cluster expansions. In: Les Houches Summer School Notes, 1984. Osterwalder, K. (Ed.)
Brydges, D., Federbush, P.: A new form of the Mayer expansion in classical statistical mechanics. J. Math. Phys.19, 2064–2067 (1978)
Brydges, D., Federbush, P.: Debye screening. Commun. Math. Phys.73, 197–246 (1980)
Cammarota, C.: Decay of correlations for infinite range interactions in unbounded spin systems. Commun. Math. Phys.85, 517–528 (1982)
Gallavotti, G., Martin-Lof, A., Miracole-Sole, S.: Some problems connected with the description of coexisting phases at low temperature in the Ising model, Battelle 1971. In: Lecture Notes in Physics. Berlin, Heidelberg, New York: Springer 1971
Glimm, J., Jaffe, A., Spencer, T.: A convergent expansion about mean field theory. Ann. Phys.101, 610–630 and 631–669 (1976)
Gruber, Ch., Lebowitz, Joel L., Martin, Ph.A.: Sum rules for inhomogeneous Coulomb systems. J. Chem. Phys.75 (2), 944–954 (1981)
Imbrie, J.: Debye screening for jellium and other Coulomb systems. Commun. Math. Phys.87, 515–565 (1983)
Jancovici, B.: Classical Coulomb systems near a plane wall. I. J. Stat. Phys.28, 43–65 (1982)
Jancovici, B.: Classical Coulomb systems near a plane wall. II. J. Stat. Phys.29, 263–280 (1982)
Jancovici, B.: Surface properties of a classical two-dimensional one-component plasma: exact results. J. Stat. Phys.34, 803–815 (1984)
Jancovici, B.: Surface correlations in a quantum mechanical one-component plasma (preprint)
Lieb, E.H., Lebowitz, J.L.: The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Adv. Math.9, 316–398 (1972)
Seiler, E.: Gauge theories as a problem of constructive quantum field theory and statistical mechanics. Lecture Notes in Physics. Berlin, Heidelberg, New York: Springer 1982
Smith, E.R.: Exact results for the electrostatic double layer at a charged boundary of the two-dimensional one-component plasma. Phys. Rev. A24, 2851 (1981)
Speer, E.: Combinatoric identities for cluster expansions (Preprint)
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
This work was supported in part by the National Science Foundation under Grants No. PHY 83-01011 and PHY 81-16101 A03
Rights and permissions
About this article
Cite this article
Federbush, P., Kennedy, T. Surface effects in Debye screening. Commun.Math. Phys. 102, 361–423 (1985). https://doi.org/10.1007/BF01209293
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01209293