1D Crossover, universality and finite-size scaling of the specific heat

We report measurements of the specific heat of ³He- ⁴He mixtures near the superfluid transition when confined to channels of 1 /tm square cross section. These data test the universality of finite-size scaling as function of ³He 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 φ μ₃ - μ₄. 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 ⁴He, both above and below T _λ. An analysis whereby the exponent a 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.