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

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