Theory of the Random Magnetic Mixture. I: Ising System

Abstract

A theory of the random magnetic mixture of some kinds of Ising spins is formulated in terms of distribution functions which are introduced for the thermal averages of each kind of spins. The distribution functions are determined from a simultaneous non-linear integral equation of order n, where n is the number of kinds of spins. By the use of this theory, the magnetic properties of a honeycomb lattice with two kinds of magnetic atoms are investigated. The ferromagnetic phase, the ferromagnetic phase and the antiferromagnetic phase are obtained with respect to the types and concentrations of those atoms. The possibilityof a new phase with the infinite susceptibility without the spontaneous magnetization is also conjectured. The magnetization process and phase transition in each phase are studied in detail.