Thermodynamics Near the Two-Fluid Critical Mixing Point in ${\mathrm{He}}^3$ - ${\mathrm{He}}^4$

The two-fluid critical mixing point in ${\mathrm{He}}^3$ - ${\mathrm{He}}^4$ differs from ordinary critical points in that it occurs at the intersection of three lines of critical points, in a suitable variable space. A free-energy function is proposed which removes certain discrepancies between classical (Landau) theory and experimental thermodynamic measurements. Certain solid-state transitions (e.g., the metamagnetic-antiferromagnetic transition in Fe${\mathrm{Cl}}_2$) are thermodynamic analogs of critical mixing in ${\mathrm{He}}^3$ - ${\mathrm{He}}^4$.