Cluster Expansion Theory for a System of Random Ising Spins

The system under consideration is N Ising spins which interact through two-body exchange interactions and are randomly distributed over NL lattice points. By means of generalized cumulant expansion method, a statistical mechanical treatment of the system is made when the concentration p(=N/NL) is sufficiently low. Thermodynamic quantities are shown to be expressed in a form of cluster expansion similar to that in the theory of classical gases. As an application of the method, nearest neighbor ferromagnetic interactions are assumed, and the critical concentration below which there is no Curie temperature is calculated for some crystal structures and is compared with the results of other theories.