Exact solution of a charge-asymmetric two-dimensional Coulomb gas

The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q(1) = + 1) and negatively (q(2) = 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) beta < 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-beta expansion and close to the collapse beta = 4 point. The comparison is made with the exactly solvable symmetric version of the model (q(1) = + 1, q(2) = -1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.