Static universality class for gadolinium

High-precision magnetization, $M(T,H),$ data have been taken along the c axis (easy direction of magnetization) of a high-purity Gd single crystal in the critical region near the ferromagnetic-paramagnetic phase transition. Elaborate data analyses demonstrate that the single power laws, by themselves, do not adequately describe the observed field dependence of M at the Curie point TC, M(TC,H), and the temperature variations of spontaneous magnetization, $M(T,0),$ and initial susceptibility, χ(T), in the asymptotic critical region |ε|=|(T-TC)/TC|<~2×10^-3, but do so only when the multiplicative logarithmic corrections (LC), predicted by the renormalization group (RG) calculations for dipolar Ising (spin dimensionality $n=1)$ spin systems at the upper marginal space dimension d*=3, are taken into account. Such data analyses also permit the first accurate determination of LC exponents (x^',x), the asymptotic critical exponents β, γ, and δ, and critical amplitudes B ̂ \^, ^Γ, and D ̂ \^ for $M(T,0),$ χ(T), and M(TC,H). The exponents x^', x, β, γ, and δ, as well as the universal amplitude ratio R_χ=D ̂ \^B^δ-1^Γ possess the same (within the uncertainty limits) values as those yielded by the RG calculations for a $d=3$ uniaxial dipolar ferromagnet. Moreover, the presently determined values of β, γ, and δ, together with the reported value of the specific heat critical exponent α, obey the scaling relations β+γ=βδ and α+2β+γ=2 accurately. By establishing that gadolinium belongs to the $d=3,$ $n=1$ dipolar static universality class, the present results resolve the long-standing controversy surrounding the nature of the asymptotic critical behavior of Gd.