Finite-size scaling of 4He at the superfluid transition

Experimental results for confined He-4 are reviewed that are relevant to correlation-length scaling near the superfluid transition. Data are discussed for which the uniform confinement represents dimensionality crossover from three dimensions (3D) to 2D, 1D, and 0D. In addition, data for the onset of superfluidity are discussed representing 2D to 1D crossover. Collectively, these data for the specific heat, superfluid density, and thermal conductivity yield, in some cases, excellent agreement with expectations of correlation-length scaling and, in others, surprising disagreement. This is especially true in the case of 3D to 2D crossover where data are most plentiful. Here there is a clear distinction between scaling when the confined helium is normal and the lack of scaling when helium becomes superfluid. By far the most problematic result is the lack of scaling for the superfluid density for 3D to 2D crossover and, to some extent, for 3D to 1D crossover. Connectivity and proximity effects can be identified with some data. These might explain some experimental results and present opportunities for further studies of weakly coupled superfluid regions. Measurements to test the universality of finite-size effects along the superfluid transition lines as function of pressure and He-3 concentration are also discussed. In the case of the specific heat, data indicate that the nonuniversal behavior of the critical exponent alpha, obtained from bulk measurements, is responsible for the observation of a distinct scaling locus for confined pure He-4 versus that of the confined mixtures.