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)
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.