A spin-1 Ising model, which simulates the thermodynamic behavior of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures along the $\lambda$ line and near the critical mixing point, is introduced and solved in the mean-field approximation. For reasonable values of the parameters of the model the phase diagram is qualitatively similar to that observed experimentally and the phase separation appears as a consequence of the superfluid ordering. Changing the parameters produces many different types of phase diagram, including as features $\lambda$ lines, critical points, tricritical points, and triple points. Certain thermodynamic features which differ from the ${\mathrm{He}}^3$-${\mathrm{He}}^4$ experiments may be artifacts of the mean-field theory.

• Received 23 March 1971

DOI:https://doi.org/10.1103/PhysRevA.4.1071