Monte Carlo simulation of a two-dimensional continuum Coulomb gas

TL;DR

This paper uses Monte Carlo simulations to explore the phase diagram of a two-dimensional Coulomb gas model, revealing the nature of vortex phase transitions at various densities and interactions.

Contribution

It provides the first comprehensive phase diagram of the 2D Coulomb gas without density restrictions, including the effects of short-range repulsion.

Findings

Kosterlitz-Thouless transition occurs at negative vortex chemical potential.

Short-distance repulsion leads to a first-order transition at high vortex density.

Phase diagrams are constructed for various vortex densities and interactions.

Abstract

We study the classical two-dimensional Coulomb gas model for thermal vortex fluctuations in thin superconducting/superfluid films by Monte Carlo simulation of a grand canonical vortex ensemble defined on a continuum. The Kosterlitz-Thouless transition is well understood at low vortex density, but at high vortex density the nature of the phase diagram and of the vortex phase transition is less clear. From our Monte Carlo data we construct phase diagrams for the 2D Coulomb gas without any restrictions on the vortex density. For negative vortex chemical potential (positive vortex core energy) we always find a Kosterlitz-Thouless transition. Only if the Coulomb interaction is supplemented with a short-distance repulsion, a first order transition line is found, above some positive value of the vortex chemical potential.