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The temperature dependence of the magnetic anisotropy of ferromagnetic materials is analyzed. Simple ferromagnets, such as Fe and Co, obey the m=n (n+1)/2 power laws predicted by the Callen and Callen [Phys. Rev. 129, 578 (1963)] theory, but in alloys, the applicability of the theory is an exception rather than the rule. Many alloys, such as the rare-earth transition-metal intermetallics and L10 magnets, violate a basic assumption of the theory, namely, that the single-ion anisotropy and the spontaneous magnetization have the same origin. This is the reason for significant deviations from the Callen and Callen behavior, such as the m=2 law we obtained for L10 alloys.