Anisotropy of a Cubic Ferromagnet at Criticality

Abstract

Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear susceptibility acquires at $T_c$ the universal value ${\delta }_4^{\ast }=\frac{2v^{\ast }}{3(u^{\ast }+v^{\ast })}$ where $u^{\ast }$ and $v^{\ast }$ -- coordinates of the cubic fixed point on the flow diagram of renormalization group equations. In the paper, the critical value of the reduced anisotropy is estimated within the pseudo-$\epsilon$ expansion approach. The six-loop pseudo-$\epsilon$ expansions for $u^{\ast }$, $v^{\ast }$, and ${\delta }_4^{\ast }$ are derived for the arbitrary spin dimensionality $n$. For cubic crystals ($n=3$) higher-order coefficients of the pseudo-$\epsilon$ expansions obtained turn out to be so small that use of simple Padé approximants yields reliable numerical results. Padé resummation of the pseudo-$\epsilon$ series for $u^{\ast }$, $v^{\ast }$, and ${\delta }_4^{\ast }$ leads to the estimate ${\delta }_4^{\ast }=0.079\pm 0.006$ indicating that detection of the anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is certainly possible.

arXiv comment19 pages, 6 tables, 1 figure

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Cited by in corpus (4)

• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Continued functions and Borel-Leroy transformation: Resummation of six-loop ε-expansions from different universality classes
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