Vortex-ring specific heat of superfluid helium in porous materials

The specific heat of superfluid He-4 in a porous material is calculated using a vortex-ring renormalization theory, both for completely filled pores and for thin films. The porous medium introduces a neu, length scale L into the problem which is of the order of the pore size of the material, and which becomes the starting vortex-ring size of the recursion relations (the T=0 correlation length). The specific heat displays a lambda-like critical peak, but the amplitude of the peak is suppressed by a very large factor (L/a(0))(3) compared to the bulk, where a(0) approximate to 2.5 Angstrom is the starting ring size for the bulk liquid calculation. This is in agreement with scaling theories invoking "two-scale-factor universality", and provides a simple picture of the superfluid transition in porous materials, where the vortex cores of the rings are the material itself.