Theory of random dilute magnets with application to MnZnF ₂

The variation of the critical temperature T$_c$ of a magnetic crystal randomly diluted with non-magnetic atoms is evaluated as a function of dilution by a method which expands the susceptibility in a power series in the concentration p and extrapolates to find the radius of convergence. The method is applied to simple ferromagnetic Bravais lattices using the Ising and the Heisenberg models with spin $\frac{1}{2}$, and compared with other methods. Values of the critical concentration when T$_c$(p) $\rightarrow$ 0 are derived and discussed in relation to those obtained from lattice statistics. The method is extended to antiferromagnetic crystals by considering the divergence of the `staggered' susceptibility. In particular, results are obtained for the MnF$_2$ lattice for comparison with experiment.