Critical behavior of coupled 4He regions near the superfluid transition

Proximity and coupling effects between contiguous regions of 4He are expected to occur over a distance on the order of the temperature-dependent correlation length ξ(t). We present recent measurements of 4He confined in arrays of ⁽2μm⁾3 boxes linked through a 4He film. The specific heat and superfluid fraction of the 4He in these geometries reveal effects which occur at distances much larger than expected. These effects include enhancements in specific heat and superfluid fraction as well as shifts in the temperatures of the superfluid onset and specific-heat maximum. Our analysis gives evidence for the relevance of the finite-size correlation length ξ(t,L) in explaining these effects even though the effects occur at distances over an order of magnitude larger than ξ(t,L). These results can be used to deduce the finite-size scaling locus for ξ(t,L). The spatial distance over which coupling and proximity effects are observed raises questions regarding the physical mechanism for these effects and the interpretation of ξ(t). Lastly, these results are discussed in connection to other measurements of 4He in confined geometries, and the relevance to other critical systems.