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Universal finite-size effects in the two-dimensional asymmetric Coulomb gas on a sphere. (English) Zbl 0969.82555

Summary: 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,\(\cdots{}\)) charges; Q=1 corresponds to the symmetric two-component plasma and the limiting case Q\(\rightarrow{}\infty{}\) 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 model’s 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.

MSC:

82D10 Statistical mechanics of plasmas
82B30 Statistical thermodynamics
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