Sine-Gordon mean field theory of a Coulomb Gas

TL;DR

This paper employs Sine-Gordon field theory to analyze the phase diagram of a neutral Coulomb gas, revealing topological similarities with Monte Carlo and DHBj theories, and detailing phase transition behaviors in 2D and 3D.

Contribution

It introduces a variational mean field approach using Sine-Gordon theory to derive phase diagrams for Coulomb gases in 2D and 3D, aligning with simulation results.

Findings

Phase diagram matches Monte Carlo and DHBj predictions.

Kosterlitz-Thouless line terminates at a tricritical point in 2D.

Insulating phase maps to zero density when transformed.

Abstract

Sine-Gordon field theory is used to investigate the phase diagram of a neutral Coulomb gas. A variational mean field free energy is constructed and the corresponding phase diagrams in two (2d) and three dimensions (3d) are obtained. When analyzed in terms of chemical potential, the Sine-Gordon theory predicts the phase diagram topologically identical with the Monte Carlo simulations and a recently developed Debye-H\"uckel-Bjerrum (DHBj) theory. In 2d we find that the infinite order Kosterlitz-Thouless line terminates in a tricritical point, after which the metal-insulator transition becomes first order. However, when the transformation from chemical potential to the density is made the whole of the insulating phase is mapped onto zero density.