Field theory and anisotropy of cubic ferromagnet near Curie point

TL;DR

This paper investigates the critical anisotropy of cubic ferromagnets near the Curie point, using advanced expansion techniques to estimate the universal anisotropy parameter and discussing discrepancies with previous results.

Contribution

It provides a numerical estimate of the critical anisotropy parameter using xpansion and pseudo-xpansion methods, clarifying discrepancies in previous calculations.

Findings

Estimated anisotropy parameter A* .13 using resummation techniques.

Found close agreement between pseudo-xpansion and five-loop xpansion results.

Identified and discussed the roots of discrepancies with six-loop xpansion analysis.

Abstract

Critical fluctuations are known to 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, effective anisotropy acquires at T_c the universal value A* = v*/u* where u* and v* are coordinates of the cubic fixed point entering the scaling equation of state and expressions for nonlinear susceptibilities. In the paper, the numerical value of the anisotropy parameter A at the critical point is estimated using the \epsilon-expansion and pseudo-\epsilon-expansion techniques. Pade resummation of six-loop pseudo-$\epsilon$-expansions for u*, v*, and A* leads to the estimate A* = 0.13 close to that extracted from the five-loop \epsilon-expansion but differing considerably from the value A* = 0.089 given by the analysis of six-loop expansions of the \beta-functions themselves. This discrepancy is discussed and its roots are cleared up.