Critical Casimir effect in superfluid wetting films

Recent experimental data for the complete wetting behavior of pure He-4 and of He-3-He-4 mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda transition and the tricritical end point, respectively, which can be attributed to critical Casimir forces f(C). We calculate the scaling functions Theta of f(C) within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of Theta deduced from the experimental data and predicts the crossover behavior between the tricritical point and the lambda transition of pure He-4 which are connected by a line of critical points. The formation of a "soft-mode" phase within the wetting films gives rise to a pronounced maximum of f(C) below the tricritical point as observed experimentally. Near the tricritical point we find logarithmic corrections similar to L-3(ln L)(1/2) for the leading behavior of Theta dominating the contributions from the background dispersion forces.