Tricritical Casimir forces and order parameter profiles in wetting films of ${}^3\text{He}$ -${}^4\text{He}$ mixtures

Tricritical Casimir forces in ${}^3\text{He}$ -${}^4\text{He}$ wetting films are studied, within mean field theory, in therms of a suitable lattice gas model for binary liquid mixtures with short–ranged surface fields. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ${}^4\text{He}$ and it allows, inter alia, for the occurrence of a vapor phase. As a result, the model facilitates the formation of wetting films, which provides a strengthened theoretical framework to describe available experimental data for tricritical Casimir forces acting in ${}^3\text{He}$ -${}^4\text{He}$ wetting films.