Scaling, dimensionality crossover, surface and edge specific heats in confined ⁴He

We have studied the superfluid transition of ⁴He in situations where the growth of the correlation length is limited by a uniform spacial confinement. Under these conditions the critical behavior attained in the thermodynamic limit is greatly modified. One expects that data for similar confinement should scale with the correlation length. This is found to be true for the specific heat in planar confinement, 2D crossover, except in the region of the specific heat maximum and on the superfluid side. The modifications due to confinement depend on the details of the geometry. Studies of the specific heat with 1D and 0D crossover show the important role played by the lower dimension. Far from the transition the details of the confining geometry reveal contributions to the specific heat which can be attributed to surfaces and edges. Comparison of experimental results with theoretical calculations show agreement in some areas and disagreement in others.