Surface correlations for two-dimensional Coulomb fluids in a disc

TL;DR

This paper analyzes two exactly solvable models of two-dimensional Coulomb fluids in a disc, focusing on surface charge correlations and confirming long-range decay behaviors predicted by electrostatics.

Contribution

It provides exact calculations of surface charge correlations in finite 2D Coulomb fluids, validating macroscopic predictions and proposing a temperature-independent boundary density correlation decay.

Findings

Surface charge correlation decays as inverse square distance.

Boundary density correlation in two-component plasma decays as the -4 power of distance.

Long-range behavior consistent with electrostatic theory.

Abstract

After a brief review of previous work, two exactly solvable two-dimensional models of a finite Coulomb fluid in a disc are studied. The charge correlation function near the boundary circle is computed. When the disc radius is large compared to the bulk correlation length, a correlation function of the surface charge density can be defined. It is checked, on the solvable models, that this correlation function does have the generic long-range behaviour, decaying as the inverse square distance, predicted by macroscopic electrostatics. In the case of a two-component plasma (Coulomb fluid made of two species of particles of opposite charges), the density correlation function on the boundary circle itself is conjectured to have a temperature-independent behaviour, decaying as the -4 power of the distance.