96-624 Aldo Procacci, Emmanuel Pereira, Armando G. M. Neves, Domingos H. U. Marchetti

Coulomb Interaction Symmetries and the Mayer Series in the Two-Dimensional Dipole Gas (179K, LaTex, plus 8 appended eps figures, see instructions in the file) Nov 25, 96

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Abstract. We study the Mayer series of the two-dimensional dipole gas in the high temperature-low density regime. Without performing any multiscale analysis, we obtain bounds showing that the Mayer coefficients are finite in the thermodynamic limit. These bounds are obtained by exploiting a particular partial symmetry of the interaction (which we name {\it $\theta$-symmetry}), already used in some problems related to the two-dimensional Coulomb gas. By direct bounds on some Mayer graphs we also conjecture that any technique based uniquely on the $\theta$-symmetry will not be sufficient to prove analyticity of the series.

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