Fractal surface dimensionality and finite-size scaling at the superfluid transition of confined He4

A connection between surface fractal dimensionality and the critical behavior of confined He4 at the superfluid transition is suggested. It is shown that in the specific case of Nuclepore filters the disagreement with bulk-correlation-length scaling can be resolved if one ascribes a fractal dimension to the confining surface of about 2.34. Explicit scaling functions for both the specific heat and the superfluid density are suggested. Measurements of adsorption isotherms for 0.2-m filters support this fractal conjecture and yield a surface dimensionality of 2.24 0.02.