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

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(H̄) of the random internal exchange fields H̄ 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 Hₑₓₜ. The very-low-temperature magnetization per impurity is predicted to be proportional to tan^-1 HₑₓₜΔ, where Δ is a temperature- and external-field-dependent width of the probability distribution.