A Phenomenological Model on the Superfluid Transition of 4He in Porous Media∗

The superfluid transition of 4He in porous media is discussed. The eigenstates of the Hamil-tonian may be localized whether the disorder is spatially correlated or not. Based on this argument we proposed a phenomenological model to describe the effects of localization on phase transitions. The system may be divided into many isolated blocks because of the localization. We calculated the superfluid density and the free energy density for the super-fluid transition according to this model. These thermodynamical quantities are described by power laws in a certain temperature region but the hyperscaling relation is violated as one can expect. The comparison of the result of this model with the experiment on the superfluid transition of 4He in gels is given. Recent experiments[1,2] about phase transitions in a disordered system show a lot of puz-zling features. These experiments had been done with 4He filled in gels, which have highly interconnected porous structures in 3-dimensional space. For the superfluid transitions the density of the superfluid displays a power law ρ = ρ0tζ below critical temperature and the exponent ζ depends on the structure of the media evidently[1]. There are two prominen