Molecular-Field Theory of a Random Ising System in the Presence of an External Magnetic Field

Abstract

The thermodynamic properties of very dilute concentrations of magnetic impurities in a nonmagnetic system and in the presence of an externally applied magnetic field are examined, using a mean-random-field approximation. The impurities are assumed to interact via a long-range potential which alternates in sign as a function of the position between the magnetic ions. A modified form of Margenau's statistical model is used to obtain the probability distribution $P\left(\overline{H}\right)$ of the random internal exchange fields $\overline{H}$ in an Ising model. The magnetization and the specific heat are obtained as integrals over the distribution of internal fields. The variation of the magnetization and the low-temperature specific heat as a function of the external magnetic field is obtained for all temperatures. The model, when applied to a dilute alloy system, shows that the excess very-low-temperature specific heat is strongly decreased by the applied magnetic field $H_{\mathrm{ext}}$. The very-low-temperature magnetization per impurity is predicted to be proportional to ${\tan }^{-1\mathrm{}}$ $\frac{H_{\mathrm{ext}}}{\Delta }$, where $\Delta$ is a temperature- and external-field-dependent width of the probability distribution.