Universal finite-size effects in the two-dimensional asymmetric Coulomb gas on a sphere

We consider an asymmetric version of a two-dimensional Coulomb gas, made up of two species of pointlike particles with positive +1 and negative −1/Q (Q=1,2,…) charges; Q=1 corresponds to the symmetric two-component plasma and the limiting case Q→∞ is related to the one-component plasma. The system lives on the surface of a sphere, and it is studied in both canonical and grand-canonical ensembles. By combining the method of stereographic projection of the sphere onto an infinite plane with the technique of a renormalized Mayer series expansion it is explicitly shown that the finite-size expansions of the free energy and of the grand potential have the same universal term, independent of modelʹs details. As a by-product, the collapse temperature and the Kosterlitz–Thouless transition point (in the limit of a vanishing hard-core attached to particles) are conjectured for any value of Q.