Coulomb gas sum rules for vortex-pair fluctuations in 2D superfluids

TL;DR

This paper investigates vortex fluctuations in 2D superfluids using simulations of the XY model, revealing linear relationships and power-law behaviors in vortex distributions across the KT transition, and applying Coulomb-gas sum rules for modeling.

Contribution

It introduces a novel analysis of vortex fluctuations via Coulomb-gas sum rules and provides detailed simulation results across the KT transition.

Findings

Linear variation of squared winding number with circle perimeter

Power-law decay in vortex separation distances

Peak in perimeter slope near the specific heat maximum

Abstract

Vortex fluctuations above and below the critical Kosterlitz-Thouless (KT) transition temperature are characterized using simulations of the 2D XY model. The net winding number of vortices at a given temperature in a circle of radius $R$ is computed as a function of $R$. The average squared winding number is found to vary linearly with the perimeter of the circle at all temperatures above and below $T_{KT}$, and the slope with $R$ displays a sharp peak near the specific heat peak, decreasing then to a value at infinite temperature that is in agreement with an early theory by Dhar. We have also computed the vortex-vortex distribution functions, finding an asymptotic power-law variation in the vortex separation distance at all temperatures. In conjunction with a Coulomb-gas sum rule on the perimeter fluctuations, these can be used to successfully model the start of the perimeter-slope peak in the region below $T_{KT}$.