Helicity Moduli Of 3-Dimensional Dilute Xy Models

The helicity moduli of various dilute, classical $\mathrm{XY}$ models on three-dimensional lattices are studied with a view to understanding some aspects of the superfluidity of $^{4}\mathrm{He}$ in Vycor glass. A spinwave calculation is used to obtain the low-temperature helicity modulus of a regularly-diluted $\mathrm{XY}$ model. A similar calculation is performed for the randomly bond-diluted and site-diluted $\mathrm{XY}$ models in the limit of low dilution. A Monte Carlo simulation is used to obtain the helicity modulus of the randomly bond-diluted $\mathrm{XY}$ model over a wide range of temperature and dilution. It is found that the randomly diluted models do agree and the regularly diluted model does not agree with certain experimentally found features of the variation in superfluid fraction with coverage of $^{4}\mathrm{He}$ in Vycor glass.