Specific heat of critical films, the Casimir force, and wetting films near critical end points

Close to continuous phase transitions with a diverging correlation length ξ, the thermal singularities of films with thickness L are governed by a universal finite-size scaling function Θ(L/ξ) of their free energy. We propose several experiments for magnetic and fluid films as well as numerical simulations which allow one to determine Θ(L/ξ). Based on field-theoretical results for Θ(L/ξ), we make quantitative predictions for the specific heat of magnetic films, of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films, and of films composed of ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixtures close to the onset of superfluidity. The critical fluctuations within fluid films lead to a long-range Casimir force between the confining walls which can be studied by an atomic-force microscope. We discuss the strength and the temperature dependence of this force for various fluid systems. The study of wetting films close to critical end points gives direct access to the full scaling function Θ(L/ξ). In this respect we discuss in detail the wetting of a substrate by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixtures close to their λ transitions as well as by binary liquid mixtures close to their critical end points.