Monte Carlo simulation of a two-dimensional continuum Coulomb gas

Abstract

We study the classical two-dimensional (2D) 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 is a first-order transition line found, above some positive value of the vortex chemical potential.