Universal Jump in the Superfluid Density of Two-Dimensional Superfluids

Abstract

We observe that recent theories of phase transitions in the two-dimensional $\mathrm{XY}$ model predict a universal jump in the superfluid density of $^{4}\mathrm{He}$ films as ${T}_{c}$ is approached from below. Specifically, we find that ${\mathrm{lim}}_{T\ensuremath{\rightarrow}{T}_{c}}\ensuremath{-}{\ensuremath{\rho}}_{s}\frac{(T)}{T}=3.52\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ g/${\mathrm{cm}}^{2}$\ifmmode^\circ\else\textdegree\fi{}K. Analogous results should hold for two-dimensional planar magnets and liquid crystals.