Summary:
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 TKT.
Reference: https://arxiv.org/pdf/2205.06371
Speaker: Dr. Karla Galdamez, theoretical physicist, adjunct professor at University of California, Santa Cruz, department of Chemistry and Biochemistry.
