The dynamic critical exponent $y$ for superfluid helium near absolute zero

We propose a new interpolation formula for the dynamic critical exponent $y$ for the mixture of liquid He$^{4}$ and He$^{3}$ at low temperatures: \begin{equation} \label{eq1} y=(1+S_{I} -\alpha )\left( {\frac{1}{d}+\frac{1}{6}} \right)\,\,\,\,, \end{equation} where $d$ is the space dimension. In the case of $d=$3, it takes the form \[ y=z\nu =\frac{3\nu }{2}=\frac{1+S_{I} -\alpha }{2}\,(\,T_{C} \ge 0,\,\,\alpha <0)\,,\,(2) \] where \begin{equation} \label{eq2} S_{I} =\left( {\frac{T_{C} }{T }} \right)^{n},\,\,T>T_{C} =T_{\lambda } \,\,, \end{equation} $n$ is some positive constant [1], $z$ is the dynamic critical exponent and $\nu $ is the critical exponent of the correlation length. New formulas~apply not only to positive~critical temperatures $Ò_{Ñ}$ but also ~to the limiting~case~$T_{C}\to $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.\textit{ Udodov V.N.} New consequences of the static scaling hypothesis at low temperatures. \underline {Physics of the Solid State}. 2015. Ò. 57. \underline {¹ 10}. Ñ. 2073-2077. DOI: \underline {10.1134/S1063783415100340}.