Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas

TL;DR

This paper demonstrates a discontinuity in the inverse dielectric constant of 2D Coulomb gases indicating a Kosterlitz-Thouless transition, and explores similar phenomena in 3D logarithmic plasmas using finite-size scaling methods.

Contribution

It introduces a numerical method to identify phase transitions in 2D and 3D logarithmic plasmas, extending the understanding of Kosterlitz-Thouless transitions to three dimensions.

Findings

Discontinuity in inverse dielectric constant in 2D Coulomb gas.

Evidence of Kosterlitz-Thouless transition in 3D logarithmic plasma.

Distinct finite-size scaling behaviors compared to 3D Coulomb gas.

Abstract

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D XY model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.