Field theory and anisotropy of a cubic ferromagnet near the Curie point

It is known that critical fluctuations can change the effective anisotropy of a cubic ferromagnet near the Curie point. If the crystal undergoes a phase transition into the orthorhombic phase and the initial anisotropy is not too strong, then the effective anisotropy acquires the universal value $A^*=v^*/u^*$ at $T_{\mathrm c}$, where $u^*$ and $v^*$ are the coordinates of the cubic fixed point of the renormalization group equations in the scaling equation of state and expressions for nonlinear susceptibilities. Using the pseudo-$\epsilon$-expansion method, we find the numerical value of the anisotropy parameter $A$ at the critical point. Padé resummation of the six-loop pseudo-$\epsilon$-expansions for $u^*$, $v^*$, and $A^*$ leads to the estimate $A^*=0.13\pm0.01$, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.