1D Crossover, Universality and Finite-Size Scaling of the Specific Heat

We report measurements of the specific heat of He-3-He-4 mixtures near the superfluid transition when confined to channels of 1 mu m square cross section. These data test the universality of finite-size scaling as function of He-3 concentration for 1D crossover. The analysis of these data requires that data measured at fixed concentration be converted to a specific heat at constant chemical potential difference phi = mu(3) - mu(4). This is carried out according to a procedure performed for planar mixtures by Kimball and Gasparini. We find that, in the most self-consistent analysis of the data, the mixtures define a separate scaling locus from that of pure He-4, both above and below T-lambda. An analysis whereby the exponent alpha is forced to have the same universal value-as opposed to the best-fit value-yields a good collapse of all the data. This is achieved, however, at a cost of self-consistency. These results mirror very closely those obtained for finite-size scaling of confined planar mixtures, i.e. for 2D crossover.