Another Derivation of a Sum Rule for the Two-Dimensional Two-Component Plasma

TL;DR

This paper derives a simple expression for the second moment of the number density correlation function in a 2D two-component plasma using diagrammatic methods, providing a new derivation of a known sum rule.

Contribution

It presents a novel derivation of the sum rule for the second moment in a 2D two-component plasma using diagrammatic techniques, offering an alternative to previous methods.

Findings

Second moment of the correlation function is $rac{1}{12 \pi [1-(rac{\Gamma}{4})]^2}$.

Derivation uses diagrammatic methods directly.

Provides a new derivation of a known sum rule.

Abstract

In a two-dimensional two-component plasma, the second moment of the number density correlation function has the simple value $\{12 \pi [1-(\Gamma/4)]^2\}^{-1}$, where $\Gamma$ is the dimensionless coupling constant. This result is derived directly by using diagrammatic methods.