2D vortex fluctuations above the critical Kosterlitz-Thouless transition temperature

Vortex fluctuations above the critical Kosterlitz-Thouless (KT) transition temperature are characterized using simulations of the 2D XY model. The asymptotic vortex-vortex correlation function is found to be a power law in the vortex separation at all temperatures. The correlation of plus-minus vortex pairs has the expected exponent of -4 at T_KT, but then rises to a sharp peak of nearly -3 at T = 1.1 T_KT, close to the specific heat peak at 1.15 T_KT. It then decreases back to the value of -4 at infinite temperature. The plus-plus and minus-minus correlations have an exponent of -4 at all temperatures. Also studied is the net winding number of vortices fluctuated in a circle of radius R. The averaged net winding number squared is found to vary linearly with the circle perimeter at all temperatures above and below T_KT, contrary to several speculations in the literature. The slope of the variation with R is found to sharply peak at a temperature close to the correlation function and specific heat peaks, and then decreases to a value at infinite temperature that is in complete agreement with an early theory by D. Dhar. These results show that significant correlations between the vortices persist even to infinite temperature.