A review of giant correlation-length effects via proximity and weak-links coupling in a critical system: 4He near the superfluid transition.

We review measurements of 4He near the superfluid transition in arrangements whereby an array of weak links couple relatively larger, more bulk-like 4He regions. In contrast to experiments which focus on the dependence of the superflow on the chemical potential difference across the links, these studies focus on the specific heat of both the weak links and that of the larger coupled regions, as well as the behavior of the superfluid fraction within the weak links. The data show unexpected results which reflect a very long range coupling as well as modification of the weak link itself due to the proximity to bulk-like helium. One finds that while the three-dimensional correlation length [Formula: see text], where [Formula: see text], is involved in these long-range effects, the distance over which these can be seen is of the order of 100 to 1000 times [Formula: see text]. These results call into question our understanding of the meaning of the correlation length at a critical point as the 'range' over which information can propagate. These studies are the first to measure the thermodynamic properties of weak links for a critical system where fluctuations are important. They differ in essential ways with expectations from mean-field considerations. We compare results with other 4He measurements, with superconductors and the theoretical calculations of the Ising model.

Three-dimensional critical behavior with 2D, 1D, and 0D dimensionality crossover: surface and edge specific heats.

The critical behavior at a second order phase transition is characterized by the divergence of the correlation length xi. We have studied the superfluid transition of 4He in a series of experimental cells in which this divergence of xi is modified due to finite-size confinement. In particular, the design of these cells is such that the smallest dimension is kept the same, 1 microm, but the geometry is such that one obtains crossover to dimensionality of 2, 1, and 0. This corresponds to films, channels, and boxes filled with helium. We measure the specific heat and compare these results with theoretical expectations. We identify surface and line specific heat contributions by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. The design of these cells is made possible by a combination of silicon lithography and direct wafer bonding.

Superfluid fraction of (3)He-(4)He mixtures confined at 0.0483 microm between silicon wafers.

We report measurements of the superfluid fraction rho(s)/rho of films of (3)He-(4)He mixtures confined between silicon wafers at 0.0483 microm separation. The data obtained using adiabatic fountain resonance (AFR) can be used to test for the first time expectations of correlation-length scaling in the case of planar mixtures. For the mixtures, the data for rho(s)/rho collapse well on a universal function. The dissipation associated with AFR can also be scaled, and indicates two-dimensional crossover. These results are in contrast to pure (4)He, where over a wider range of confinements, the data for rho(s)/rho are found not to scale.