Mean field theory for Coulomb systems

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Abstract

We study a classical charge symmetric system with an external charge distribution q in three dimensions in the limit that the plasma parameter e{open}→ zero. We prove that if q is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean field Ψ(x) where Ψ is given by-ΔΨ+ 2z sinh(βΨ) =q This is the mean field equation of Debye and Hückel. The proof uses the sine-Gordon transformation, the Mayer expansion, and a correlation inequality.

Original languageEnglish (US)
Pages (from-to)529-559
Number of pages31
JournalJournal of Statistical Physics
Volume37
Issue number5-6
DOIs
StatePublished - Dec 1 1984
Externally publishedYes

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Keywords

  • Coulomb systems
  • Debye-Hückel theory
  • Mayer expansion
  • mean field theory
  • sine-Gordon transformation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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