Helium in Vycor, constrained randomness, and the Harris criterion

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.