Scaling of the magnetic permeability at the Berezinskii-Kosterlitz-Thouless transition from Coulomb gas simulations

TL;DR

This study uses Monte Carlo simulations and finite size scaling to analyze the Berezinskii-Kosterlitz-Thouless transition in a Coulomb gas model, revealing how vortex configurations and scaling corrections influence magnetic permeability near the transition.

Contribution

It introduces a method to relax the neutrality condition in Coulomb gas simulations, enabling the calculation of magnetic permeability and detailed scaling analysis of vortex fluctuations.

Findings

Vortex number fluctuations exhibit remarkable scaling at the transition.

Multiplicative scaling corrections significantly affect vortex fluctuation behavior.

Including higher-order corrections improves the accuracy of critical property determination.

Abstract

A new approach to the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional Coulomb gas model is explored by MC simulation and finite size scaling. The usual mapping of a neutral two-dimensional superconductor in zero magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction between the vortices, and with periodic boundary conditions vortex configurations are always vorticity neutral with an equal number of plus and minus vortices. We demonstrate that relaxing the neutrality condition has certain advantages. It leads to non-neutral vortex configurations that can appear in real systems with open boundary conditions and permits calculation of the compressibility, which for thin film superconductors corresponds to the magnetic permeability. The vortex-number fluctuation has remarkable scaling properties at and below the Berezinskii-Kosterlitz-Thouless transition. The fugacity variable becomes dangerously irrelevant in the low-temperature phase and leads to a multiplicative scaling correction to the mean-square vortex-number fluctuation and to the magnetic permeability. This multiplicative correction strongly affects the scaling properties of the vorticity fluctuation at and below the transition. Consequences of these findings are demonstrated using Monte Carlo simulations. Inclusion of the next-higher order correction to scaling is found to play an important role in the analysis of numerical data for the vortex number fluctuation and permits accurate determination of the critical properties.