Phase diagram of fluid phases in {}³He -{}⁴He mixtures

Fluid parts of the phase diagram of ${}^3$He -${}^4$He mixtures are obtained from a mean-field analysis of a suitable lattice gas model for binary liquid mixtures. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ${}^4$He and includes the occurrence of vacancies. This latter degree of freedom allows the model to exhibit a vapor phase and hence can provide the theoretical framework to describe the experimental conditions for measurements of tricritical Casimir forces in ${}^3$He -${}^4$He wetting films.