Coulomb gas sum rules for vortexpair fluctuations in 2D superfluids
Abstract
Vortex fluctuations above and below the critical KosterlitzThouless (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 vortexvortex distribution functions, finding an asymptotic powerlaw variation in the vortex separation distance at all temperatures. In conjunction with a Coulombgas sum rule on the perimeter fluctuations, these can be used to successfully model the start of the perimeterslope peak in the region below $T_{KT}$.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.06371
 Bibcode:
 2022arXiv220506371F
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Quantum Gases;
 High Energy Physics  Lattice
 EPrint:
 Typo corrections, 5 pages, 5 figures