Thermodynamic derivatives in3He-4He mixtures in the critical region of the superfluid transition

By assuming a phenomenological Ginzburg-Landau-Wilson free energy for³He-⁴He mixtures near the critical surface of the superfluid transition we can express thermodynamic derivatives of the form (?a/?b) _c,d in terms of a correlation function of ¦ψ¦², where Gy is the order parameter. Herea, b, c, and d are any four of the quantities entropys, number densityn, molar concentrationX, temperatureT, pressurep, and chemical potential difference Δ=μ₃?μ₄. Relationships among these thermodynamic derivatives are those of the Pippard-Buckingham-Fairbank approximation in the³He-⁴He case. Some combinations of the coefficients in the free energy are equal to derivatives on the critical surface and remain invariant with respect to renormalization group transformations. A general scheme is also developed to give correlation function expressions for thermodynamic derivatives.