Thermodynamics Near the Two-Fluid Critical Mixing Point in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Abstract

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 ${\mathrm{He}}^{3}$ - ${\mathrm{He}}^{4}$.