The two-dimensional two-component plasma plus background on a sphere : Exact results

TL;DR

This paper provides an exact solution for a two-dimensional Coulomb gas with background on a sphere at a specific temperature, calculating correlations and grand potential, and analyzing finite-size effects.

Contribution

It presents the first exact solution for a generalized 2D Coulomb gas with background on a sphere at a special temperature.

Findings

Correlation functions are explicitly calculated.

Grand potential exhibits universal finite-size correction.

Thermodynamic limit behavior is characterized.

Abstract

An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value $\Gamma = 2$ of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out~: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.