Results for the phase diagram of the two-dimensional Coulomb gas

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Abstract
A derivation of a self-consistent set of renormalization equations for the two-dimensional Coulomb gas is given within a systematic approximation scheme. Results for the phase-transition properties of the Coulomb gas are inferred from high-precision numerical integration of these equations. Connections to and extensions of earlier-known results are given. Critical exponents for a new critical point in the phase diagram are calculated from the equations and are found to correspond to those of a Ginzburg-Landau model in a Gaussian approximation. It is suggested that the true character of the new critical point is of Ising type.