Experimental verification of scaling and test of the universality hypothesis from specific-heat data

Through a careful analysis of recently reported specific-heat data for several Heisenberg-like and dipolar-dominated magnetic systems and of new data for iron, the hypotheses of scaling and universality are tested. A comparison of the data above $T_c$ with that below $T_c$ verifies the scaling law $\alpha ={\alpha }^{\prime }$ without first performing computer fits to explicitly determine values for the exponents. After obtaining values for the critical index $\alpha ={\alpha }^{\prime }$ and the amplitude ratio $\frac{A^{+}}{A^{-}}$, we test the assertion that these quantities are universal in that they depend only upon $d$ and $n$. Our results show that the Heisenberg ferromagnets all belong to the same universality class, falling within $1\frac{1}{2}$ standard deviations of the values $\frac{A^{+}}{A^{-}}=1.11\mathrm{}\pm 0.09$ and $\alpha ={\alpha }^{\prime }=-0.10\mathrm{}\pm 0.01$, whereas the antiferromagnet RbMn${\mathrm{F}}_3$ departs from universal behavior with higher values for $\frac{A^{+}}{A^{-}}$ and $\alpha$, more than three standard deviations from the mean values for the ferromagnets. Characteristic dipolar behavior has been found in EuO and in four Cu salts, and their small negative exponents are in good agreement with the recent prediction of Fisher and Aharony.