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

Abstract

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_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-ϵ-expansion method, we find the numerical value of the anisotropy parameter A at the critical point. Padé resummation of the six-loop pseudo-ϵ-expansions for u*, v*, and A* leads to the estimate A* = 0.13 ± 0.01, giving evidence that observation of anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is entirely possible.