Scaled-equation-of-state analysis of the specific heat in fluids and magnets near critical point

Scaled equations of state for fluids and magnets are studied near the critical point, with particular emphasis on specific-heat predictions. The important of fitting both the exponent and the critical amplitudes is emphasized. Previous proposals, such as the Missoni, Levelt Sengers, and Green (MLSG) and "linear-model" equations are examined, and the corresponding amplitude ratio $\frac{A}{A^{\prime }}$ calculated as a function of the parameters. The linear model is found to be inapplicable to Heisenberg-like systems in which the exponent $\alpha$ is negative, and $\frac{A}{A^{\prime }}>1\mathrm{}$. Specific-heat data on Xe, C${\mathrm{O}}_2$, Ni, and EuO are compared to predictions based on the MLSG and linear-model equations, with parameters previously determined using pressure, volume, and temperature ($\mathrm{PVT}$) and magnetization, field, and temperature ($\mathrm{MHT}$) data. There is a small but probably significant discrepancy for the fluids, and a large deviation in the magnetic case. A "modified MLSG" equation is proposed, with an additional parameter, by means of which both $\mathrm{PVT} \mathrm{}\left(\mathrm{MHT}\right)\mathrm{}$ and specific-heat data may be fitted. Using this equation, an estimate is made for the effect of small fields on rounding the specific-heat singularity in magnetic systems. In EuO it is found that a field as small as the earth's field has a perceptible effect on the specific heat rounding near $T_c$.