Short-distance expansion of correlation functions in the charge-symmetric two-dimensional two-component plasma: Exact results

TL;DR

This paper provides exact results for the short-distance behavior of correlation functions and effective interactions in a two-dimensional charge-symmetric Coulomb gas, valid across the stability regime where Coulombic coupling is less than 2.

Contribution

It derives exact short-distance asymptotics for correlation functions, effective potentials, and density profiles in the 2D two-component plasma for a broad range of parameters.

Findings

Exact short-distance asymptotics of density correlation functions.

Short-distance behavior of effective interactions between external charges.

Density profiles near an external charge in the plasma.

Abstract

We determine exactly the short-distance leading behavior of the density correlation functions of a two-dimensional two-component charge-symmetric Coulomb gas composed of point particles, in the whole regime of stability where the coulombic coupling $\beta<2$. More generally, we compute the short-distance behavior of the effective interaction potential between two external arbitrary charges $Q_1$ and $Q_2$ immersed in the plasma, for $\beta |Q_1|<2$ and $\beta |Q_2|<2$. We also find the short-distance asymptotics of the density profiles near a single external charge $Q$ immersed in the plasma for $\beta |Q|<2$.