Ising Ferromagnets with Random Impurities

Abstract

The Ising of spin 1/2 with the nearest-neighbor interaction, in which nonmagnetic impurity atoms are dissolved, is investigated. Based on the identity < s i >=<tanh ( K Σ s j )>, decoupling approximation is introduced for treating the many-spin correlation functions. The dependences of the critical temperature and of the spontaneous magnetization on the impurity concentration are calculated for two- and three-dimensional lattices. The results for the critical temperature and the critical concentration are better than the results of the results of the extended molecular-field approximations of Mamada and Takano, or of Oguchi and Obokata. Especially for the three-dimensional lattices the critical obtained agrees with that of Sykes and Essam, estimated from the series expansion.