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

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.