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Superfluid Transition of 4He in Fractal Media

The superfluid transition of 4He in some porous media is studied through a fractal model. We incorporate the fractal aspects of the medium in both the Harris criterion and the hyperscaling relations, so that the experimentally observed nonbulk exponents can be consistently explained as resulting from a crossover to new behaviour. Available data for aerogel suggest that the superfluid transition in this case is a fractal surface (as opposed to volume) phenomenon, which can be modelled microscopically by means of an inhomogeneous effective mass. The implications of this model for the transition in xerogels and in Vycor are discussed.