Critical Casimir force in the superfluid phase: effect of fluctuations

We have considered the critical Casimir force on a $^4$He film below and above the bulk $λ$ point. We have explored the role of fluctuations around the mean field theory in a perturbative manner, and have substantially improved the mean field result of Zandi et al [Phys. Rev. E {\bf 76}, 030601(R) (2007)]. The Casimir scaling function obtained by us approaches a universal constant ($-\frac{ζ(3)}{8π}$) for $T\lesssim 2.13~\text{K}$.

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