Universality of the specific heat of Heisenberg magnets near the critical temperature

Abstract

Specific-heat measurements for the Heisenberg magnets RbMn${\mathrm{F}}_{3}$, Fe, Ni, and EuO near their magnetic-phase-transition temperatures ${T}_{c}$ are reanalyzed. We use the theoretically predicted constraints that the specific-heat exponents $\ensuremath{\alpha}$ and ${\ensuremath{\alpha}}^{\ensuremath{'}}$ above and below ${T}_{c}$ be equal to each other and that ${C}_{p}$ be continuous at ${T}_{c}$. When these constraints result in systematic deviations of the data from the fitting function, we assume that the deviations are caused by sample inhomogeneities. For those cases we discard as much of data near ${T}_{c}$ as is necessary to obtain a statistically satisfactory fit. An analysis in terms of a pure power law yields values for the amplitude ratio $\frac{A}{{A}^{\ensuremath{'}}}$ which cover a considerably smaller range than some previous analyses by others had indicated. However, there remain significant, systematic trends in $\frac{A}{{A}^{\ensuremath{'}}}$ and in $\ensuremath{\alpha}$ which can be correlated with the relative strength of the dipolar contribution to the interaction. These trends are inconsistent with estimates of these parameters based on renormalization-group theory. We consider the possibility that the inconsistency is caused by crossover effects associated with the presence of both isotropic short-range and dipolar interactions. These effects may result in effective values for $\ensuremath{\alpha}$ and $\frac{A}{{A}^{\ensuremath{'}}}$ which are not representative of either of the pure systems. We attempt to take crossover behavior into consideration by fitting the data to a function which, in addition to the leading singularity, includes a confluent singularity. With this function, a fairly wide range for the value of the leading exponent is allowed by the data for each material. We choose $\ensuremath{\alpha}=\ensuremath{-}0.14$. This value is based on measurements and a pure-power-law fit for the short-range-force system RbMn${\mathrm{F}}_{3}$, but theoretical estimates indicate that the leading exponent is numerically very similar for the dipolar case. The resulting amplitude ratios for the dipolar materials EuO and Ni are equal to each other within their uncertainties. They differ significantly from the value characteristic of short-range-force systems as represented by RbMn${\mathrm{F}}_{3}$. This difference agrees with renormalization-group estimates for the difference between the values of $\frac{A}{{A}^{\ensuremath{'}}}$ for the two cases.