The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved

TL;DR

This paper provides an exact solution to the classical two-dimensional Coulomb gas model, revealing detailed thermodynamic properties and correlation behaviors through its equivalence with the integrable sine-Gordon field theory.

Contribution

It offers the first exact analytical solution for the 2D Coulomb gas across all temperature ranges, connecting it to integrable field theory methods.

Findings

Exact bulk thermodynamics derived

Surface thermodynamics characterized

Large-distance correlation functions analyzed

Abstract

The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics, and the large-distance asymptotic behavior of the two-body correlation functions.