XY model and the superfluid density in two dimensions

By computing the incremental free energy of the two-dimensional XY model in a state with a long-wavelength twist of the local short-range order, we evaluate for all T<T_c the superfluid density ρ_s for superfluid systems. Spin-wave excitations in the XY model imply a substantial (nonuniversal) depletion of ρ_s at low temperatures. We find that these contributions do not affect the asymptotic universality; as T-->T_c^-, ρ_sT becomes universal and we recover the previous results of Nelson and Kosterlitz. In the Appendix we derive the Kosterlitz recursion relations by transforming to a sine-Gordon system and using conventional momentum shell integration techniques.