On the magnetically dilute Heisenberg and Ising ferromagnetics

The lowering of the Curie temperature of a ferromagnetic substance by random dilution with non-magnetic elements is studied on the basis of Heisenberg and Ising models having nearest-neighbour interactions between magnetic elements only. It is proved that the limiting concentration, p c, of magnetic elements, below which there is no Curie temperature, is the same for all such models, whether Heisenberg or Ising and regardless of the spin value concerned: it depends only on the lattice structure. Numerical estimates of p c are given for various lattices. Successive approximations are developed to the full Curie temperature curve, and it is found that whereas for the Ising model T c(p) approximates to pT c(1) near p=1, T c(p)<pT c(1) for the Heisenberg model.