Statistical Mechanical Theory of a Random Ferromagnetic System

The behavior of solid solutions of paramagnetic impurities which are exchange coupled in a nonmagnetic substrate turns out to yield a considerable body of information with regard to the nature of the exchange coupling as well as detailed temperature dependence of the spin system. In the present paper, a rigorous expansion of the mean free energy averaged over random sites is presented. It is shown that a ferromagnetic phase transition does occur. The Curie point is given as a function of concentration for the case of weak dilution in an implicit power series form. Many interesting qualitative features arise in the study of these systems. If the curve of magnetic moment vs temperature has inflections this indicates short-range exchange forces, whereas smooth curves indicate long-range forces. Similarly, long-range forces give rise to smooth behavior of the Curie point as a function of concentration for dilute samples. Alternatively, short-range forces give rather violent changes in Curie point near atomic fractions (numberofnearestneighbors) ^-1. The method of series development used in this paper gives rise to this expected qualitative behavior and also enables one to make quantitative prediction if the exchange potential is known. Consideration is also given to the antiferromagnetic analog together with a discussion of expected behavior of such systems in a resonance experiment.