Aspects of One-Dimensional Coulomb Gases

TL;DR

This paper reviews recent exact solutions of one-dimensional Coulomb gas models using field-theoretic methods, providing insights into the accuracy of various approximation theories for these systems.

Contribution

It introduces exact solutions for three different 1D Coulomb gas models, enabling assessment of approximation methods like Poisson-Boltzmann and strong coupling theories.

Findings

Exact solutions for 1D Coulomb gas models are obtained.

These solutions help evaluate the accuracy of common approximation methods.

The models include soap film, counterions between charged surfaces, and ionic liquid lattice capacitors.

Abstract

In this short review, we discuss recent advances in exact solutions of models based on a one- dimensional (1D) Coulomb gas by means of field-theoretic functional integral methods. The exact solutions can be used to assess the accuracy of various approximations such as the weak coupling Poisson-Boltzmann theory as well as the strong coupling theory of Coulomb gases. We consider three different 1D models: the Coulomb fluid configuration in the case of the soap film model consisting of positively and negatively charged particles between adsorbing boundaries, counterions between two charged surfaces, and an ionic liquid lattice capacitor with positively and negatively charged particles on a lattice between one positive and one negative bounding surface.