Critical point coupling in liquid helium and the significance of the correlation length

\newcommand{\boxes}[1]{$\left( #1~\mu \rm{m} \right)^3$} Recent measurements of liquid helium confined to \boxes{2} boxes connected through a 33~nm film have shown coupling effects between boxes spaced distances much larger than the correlation length $\xi(t,L)$[1,2] and proximity effects on the connecting film[3]. An analysis of data suggests that $\xi(t,L)$ is the relevant parameter in these effects. This dependence on $\xi(t,L)$ is used to argue that the enhancement in the specific heat due to coupling is a reflection of the finite-size correlation length in the boxes and hence its scaling function. All this raises some profound questions about our physical understanding of $\xi(t,L)$. \\[4pt] [1] Perron J~K, Kimball M~O, Mooney K~P and Gasparini F~M 2010 {\em Nat. Phys.\/} {\bf 6} 499--502\\[0pt] [2] Perron J~K, and Gasparini F~M 2011 {\em submitted to PNAS\/}\\[0pt] [3] Perron J~K, and Gasparini F~M 2011 {to be published in \em JPCS\/}