Two-dimensional one-component plasma on a Flamm's paraboloid

TL;DR

This paper analyzes a classical 2D one-component plasma on a Flamm's paraboloid surface at a special Coulomb coupling, providing exact solutions and detailed thermodynamic properties.

Contribution

It presents the first exact analytical solution for the plasma on a curved surface at Coulomb coupling Gamma=2, including free energy and density profiles.

Findings

Helmholtz free energy asymptotic expansion derived

Density profiles studied in various thermodynamic limits

Exact solvability at Coulomb coupling Gamma=2 achieved

Abstract

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Gamma=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.