On the two-dimensional Coulomb gas

Abstract

This is a sequel to a recent work of Gaudin, who studied the classical equilibrium statistical mechanics of the two-dimensional Coulomb gas on a lattice at a special value of the coupling constantГ such that the model is exactly solvable. This model is briefly reviewed, and it is shown that the correlation functions obey the sum rules that characterize a conductive phase. A related model in which the particles are constrained to move on an array of equidistant parallel lines has simpler mathematics, and the asymptotic behavior of its correlation functions is studied in some detail. In the low-density limit, the lattice model is expected to have the same properties as a system of charged, hard disks; the correlation functions, internal energy, and specific heat of the latter are discussed.