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We review measurements of alt;supagt;4alt;/supagt;He near the superfluid transition ina#13; arrangements whereby an array of weak links couple relatively larger, more bulk-a#13; like alt;supagt;4alt;/supagt;He regions. In contrast to experiments which focus on the dependence ofa#13; the superflow on the chemical potential difference across the links, these studiesa#13; focus on the specific heat of both the weak links and that of the larger coupleda#13; regions, as well as the behavior of the superfluid fraction within the weak links.a#13; The data show unexpected results which reflect a very long range coupling asa#13; well as modification of the weak link itself due to the proximity to bulk-likea#13; helium. One finds that while the three-dimensional correlation length ξ(t), wherea#13; t = |1 − T/Talt;subagt;λalt;/subagt;|, is involved in these long-range effects, the distance over whicha#13; these can be seen is of the order of 100 to 1000 times ξ(t). These results call intoa#13; question our understanding of the meaning of the correlation length at a criticala#13; point as the 'range' over which information can propagate. These studies area#13; the first to measure the thermodynamic properties of weak links for a criticala#13; system where fluctuations are important. They differ in essential ways witha#13; expectations from mean-field considerations. We compare results with other alt;supagt;4alt;/supagt;Hea#13; measurements, with superconductors and the theoretical calculations of the Isinga#13; model.

The second-order phase transition of 4He from a normal fluid to a superfluid is ideally suited for studies of critical behaviour. In particular, effects of confinement have been studied recently to verify theoretical predictions of correlation-length scaling and calculations of specific scaling functions. These predictions are summarized for the specific heat and the superfluid density. The method of achieving confinement is discussed, as well as the measuring technique. The specific heat and the superfluid density in planar confinement are examined. It is found that the specific heat scales well on the normal side, and just as well on the superfluid side until the region of the specific heat maximum is reached. Here deviations from scaling are seen. It is possible that this behaviour is associated with the specific crossover in two dimensions. The superfluid fraction, which has been measured for the same type of confinement in two different ways, does not scale. Results of a calculation for the superfluid density to assess the role of the inhomogeneity induced by the van der Waals attraction at the confining walls are presented.

Recently, it was shown that two confined regions of liquid 4He exhibit a proximity effect over distances much larger than the correlation length ξ[1; 2]. Here we report measurements of the superfluid fraction ρs/ρ and specific heat cp of a 33.6 nm film. Comparison with previous data from a 31.7 nm film in contact with an array of 34 × 106 (2 μm)3 boxes of 4He allows us to show quantitatively the enhancement in ρs/ρ and cp due to the presence of the boxes in the temperature region where the film orders. The enhancement in ρs/ρ is observed up to distances 650 times the bulk correlation length. This anomalously large length scale is analogous to a giant proximity effect observed in High-Tc superconductors (HTSC)[3].

Finite-size scaling theory predicts that uniformly small critical systems that have the same dimensionality and belong to the same universality class will scale as a function of the ratio of the spatial length L to the correlation length ζ. This should occur for all temperatures within the critical region. Measurements of the heat capacity of liquid 4He confined to a two-dimensional (2D) planar geometry agree well with this prediction when the 4He is normal but disagree near the specific heat maximum where the confined 4He becomes superfluid. Data for 4He confined to 1D structures show a similar behavior (however the lack of data collapse is not as dramatic). Recent measurements of the heat capacity from two 0D confinements, which differ by a factor of two in size, fail to scale at any temperature within the critical region. This lack of scaling may be due to the interaction of neighboring boxes through the shallow channels used to fill them. This is quite surprising since the liquid in the channels is not superfluid at the temperatures of interest for the helium in the boxes. Furthermore, measurements of the superfluid density of the helium within the channels reveal a critical temperature that is higher than expected suggesting that the normal fluid is affected by the already superfluid regions at each end of these channels. Both of these anomalies might be explained by a proximity effect analogous to what is seen when normal metals are sandwiched between two superconductors.

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 = 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 Tλ. 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.