Critical Concentrations in Magnetism

In the application of the Bethe-Peierls-Weiss method to dilute magnetism, Smart has exaggerated the interaction between a cluster and its surroundings by retaining the uniform molecular field. The calculation is improved by allowing the molecular field to vary from site to site on the first shell of the cluster, thereby taking into account the fact that this interaction is sensitive to the relative location of magnetic atoms in the first shell of the cluster and in the surrounding layer. For the three-dimensional lattices treated, the critical concentration is very nearly $\frac{2}{z}$, where $z$ is the coordination number of the lattice.