Abstract
We study a classical charge symmetric system with an external charge distributionq in three dimensions in the limit that the plasma parameter ɛ→ zero. We prove that ifq is scaled appropriately then the correlation functions converge pointwise to those of an ideal gas in the external mean fieldΨ(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.
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Work partially supported by NSF Grant MCS 82-02115.
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Kennedy, T. Mean field theory for Coulomb systems. J Stat Phys 37, 529–559 (1984). https://doi.org/10.1007/BF01010494
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DOI: https://doi.org/10.1007/BF01010494