The use of neutron scattering techniques to study problems in statistical mechanics is illustrated by describing recent experiments on magnetic-non-magnetic transition metal fluorides. The concentration of the magnetic ions is chosen to be close to the percolation point for the onset of long-range magnetic order. The results have confirmed that the percolation point is a multicritical point at which the long-range order may be destroyed by either geometrical or thermal disorder. The temperature scale of the thermal disorder is determined by the one-dimensional weak links in the large clusters. Results are obtained for the exponents in systems of dimensionality two and three, and with Ising and Heisenberg symmetry. In some systems the results agree with theoretical predictions, but there remain some discrepancies between theory and experiment and some aspects of the results which are not yet understood.