Critical exponents z and ν for superfluid helium near absolute zero

We propose a new interpolation formula for the dynamic critical exponent z for the mixture of liquid He4 and He3 at low temperatures:
z=(d/2)+[(1+d)(1-S_I)]/(2ν), T→T_C ≥0, α≤0,
S_I =(T_C/T)ⁿ , (1)
where d is the space dimension, n is some positive constant [1], ν is the critical exponent of the correlation length, α is the critical exponent of the heat capacity. In the case of T_C=0 we have
z=d, ν=(1+d)/d, T→T_C=0 . (2)
For d =3 we find
z=3, ν=4/3, T→T_C=0 . (3)
This value of z is twice the usual result for T_C>0.
New formulas (1) apply not only to positive critical temperatures but also to the limiting case T_C →0, which realizes in a mixture of liquid helium isotopes. The results can be applied to the systems with multi-component order parameter, when the thermodynamic potential depends on the sum of the squares of the components. Examples include Heisenberg ferromagnets and systems undergoing quantum phase transitions.
1. Udodov V.N. New consequences of the static scaling hypothesis at low temperatures. Physics of the Solid State. 2015. 57. 10. . 2073-2077. DOI: 10.1134/S1063783415100340.