SUPERFLUID-HELIUM IN FULLY SATURATED POROUS-MEDIA

The flow of superfluid He-4 through spongelike media at full saturatio n is modeled by the flow of current through an Ohmic network with rand om resistors. Solving Kirchhoff's equations leads to the conclusion th at the superfluid critical point is a percolation threshold, with crit ical exponent 1.7. The fractal dimension of the percolating cluster is 2.6. These lead to a specific-heat exponent alpha = -5.4, by the Jose phson hyperscaling relation. Existing experiments apparently do not co ver the critical region. Instead, they measure ''mean-field'' exponent s, whose values for Vycor, aerogel, and xerogel can all be reproduced by choosing appropriate distribution functions for the resistors.