Non-Hermitian Fermion Mapping for One-Component Plasma

TL;DR

This paper maps the 2D one-component plasma onto a non-Hermitian fermionic field theory, revealing a free theory at a specific temperature and identifying a phase transition at higher interaction strengths, with extensions to curved spaces.

Contribution

It introduces a novel fermionic field theory mapping for the plasma and analyzes its properties, including phase transitions and curvature effects.

Findings

Correlation functions are explicitly calculated.

A phase transition occurs at large 2.

Extensions to spaces of constant negative curvature are presented.

Abstract

The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $\beta=2$, the field theory is free. Correlation functions are calculated and a perturbation theory is discussed for extending to other $\beta$. A phase transition is found at the mean-field level at large $\beta$. Some results are extended to spaces of constant negative curvature.