Coulomb gas, dipoles and a generalization of the Debye-Hukkel approximation through the path integral representation

TL;DR

This paper reformulates the Coulomb gas partition sum using path integrals, rederives the Debye-Hukkel result, and extends it to Coulomb gases with dipoles, providing a broader theoretical framework.

Contribution

It introduces a path integral approach to Coulomb gases and generalizes the Debye-Hukkel approximation to include dipolar interactions.

Findings

Path integral formalism reproduces known results

Debye-Hukkel approximation extended to dipolar Coulomb gases

Discussion on interaction potential ranges for the approximation

Abstract

The Coulomb gas partition sum is rewritten in terms of the path integrals formalism. It is shown that perturbation theories based on the Mayer expansion and on the path integrals method lead to the identical results. The well known Debye-Hukkel result for the case of 3D Coulomb plasma is completely rederived. An analogous result is obtained for the case of the Coulomb gas with dipoles. This result can be considered as a generalization of the Debye-Hukkel approximation. Other possible generalizations including the range of interaction potentials for which the Debye-Hukkel approximation can be applyed are discussed.