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 ${\lim }_{T\to T_c}-{\rho }_s\frac{\mathrm{}\left(T\right)\mathrm{}}{T}=3.52\mathrm{}\times {10}^{-9\mathrm{}}$ g/${\mathrm{cm}}^2$°K. Analogous results should hold for two-dimensional planar magnets and liquid crystals.