Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q1 = +1) and negatively (q2 = −1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) β < 4. The mapping of the Coulomb gas is made onto the complex Bullough-Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small-β expansion and close to the collapse β = 4 point. The comparison is made with the exactly solvable symmetric version of the model (q1 = +1, q2 = −1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.