Critical Behavior and Scaling of Confined ⁴He

This chapter discusses the expected scaling behavior of helium confined in a uniform, well-defined geometry. By way of example two models are discussed—the two-dimensional (2D) Ising model and the ideal Bose gas model—to see how scaling is actually realized. A description of various experiments designed to test scaling theory, both in the case of films with a free surface and in the case of complete confinement is given. These experiments to other studies of confined helium in powders and porous glasses are compared. With liquid helium, it is easy to realize a situation of a homogeneous film consisting of a fraction of an atomic layer to a few atomic layers. Such a film becomes superfluid at a temperature well below T_λ and displays critical behavior quite different from the bulk system. The heat capacity has a power-law behavior in three dimensions with an exponent close to zero. In two dimensions, the heat capacity is expected to have a broad maximum at a temperature above the transition into the superfluid state.