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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<T₂ the superfluid density ₒ for superfluid systems. Spin-wave excitations in the XY model imply a substantial (nonuniversal) depletion of ₒ at low temperatures. We find that these contributions do not affect the asymptotic universality; as TT₂^{-}, {ₒ}T 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.
Ohta et al. (Sun,) studied this question.
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