On the magnetically dilute Heisenberg and Ising ferromagnetics

Abstract

The dependence of Curie point, θ _c, on magnetic concentration, p, is investigated, for the randomly dilute ferromagnetic Heisenberg spin 1/2 problem, by considering successive approximations to 1/χ=0, where χ is the susceptibility. This extends to the next approximation work previously reported by the authors. The simple cubic and body-centred cubic lattices are dealt with in detail. It is concluded that the behaviour of θ _c(p) for small p is not yet fully established: it is possible that the critical concentration p _c, below which there is no ferromagnetic behaviour, is greater for the Heisenberg model than for the corresponding Ising model (where it is the analogous site percolation problem critical probability).