Exact finite-size study of the 2D OCP at Γ = 4 and Γ = 6

Abstract

An exact numerical study is undertaken into the finite-N calculation of the free energy and distribution functions for the two-dimensional one-component plasma. Both disk and sphere geometries are considered, with the coupling Γ set equal to 4 and 6. Extrapolation of our data for the free energy is consistent with the existence of a universal term (χ/12) log N, where χ denotes the Euler characteristic of the surface, as predicted theoretically. The exact finite-N density profile is shown to give poor agreement with the contact theorem relating the density at contact and potential drop to the pressure in the thermodynamic limit. This is understood theoretically via a known finite-N version of..