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Debye–Hückel theory for two-dimensional Coulomb systems living on a finite surface without boundaries

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  • Téllez, Gabriel

Abstract

We study the statistical mechanics of a multicomponent two-dimensional Coulomb gas which lives on a finite surface without boundaries. We formulate the Debye–Hückel theory for such systems, which describes the low-coupling regime. There are several problems, which we address, to properly formulate the Debye–Hückel theory. These problems are related to the fact that the electric potential of a single charge cannot be defined on a finite surface without boundaries. One can only properly define the Coulomb potential created by a globally neutral system of charges. As an application of our formulation, we study, in the Debye–Hückel regime, the thermodynamics of a Coulomb gas living on a sphere of radius R. We find, in this example, that the grand potential (times the inverse temperature) has a universal finite-size correction 13lnR. We show that this result is more general: for any arbitrary finite geometry without boundaries, the grand potential has a finite-size correction (χ/6)lnR, with χ the Euler characteristic of the surface and R2 its area.

Suggested Citation

  • Téllez, Gabriel, 2005. "Debye–Hückel theory for two-dimensional Coulomb systems living on a finite surface without boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(1), pages 155-171.
    • Handle: RePEc:eee:phsmap:v:349:y:2005:i:1:p:155-171
    DOI: 10.1016/j.physa.2004.10.014
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    References listed on IDEAS

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    1. Jancovici, Bernard & Trizac, Emmanuel, 2000. "Universal free energy correction for the two-dimensional one-component plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 241-245.
    2. Lévesque, Suzanne & Paquin, Lloyd, 1986. "Les microfondements de la macroéconomique : une recension critique," L'Actualité Economique, Société Canadienne de Science Economique, vol. 62(4), pages 597-619, décembre.
    3. Jancovici, B. & Kalinay, P. & Šamaj, L., 2000. "Another derivation of a sum rule for the two-dimensional two-component plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 260-267.
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