The dynamics of very dilute Heisenberg systems

A study of the zero-temperature two-dimensional ferromagnetic and antiferromagnetic densities of states for Heisenberg spin systems which are randomly diluted is made using the computer simulation of Alben and Thorpe (1976). The prominent features of these systems at <or approximately=25% magnetic concentration are shown to be accounted for by clusters of up to five spins. As the Alben-Thorpe simulation relies on linearised equations of motion, an attempt is made to understand the limitations of this procedure at concentrations where doublet and triplet scattering is dominant. For ferromagnets the linearised equations of motion are exact, whilst for antiferromagnets they become exact as S to infinity but lead to considerable errors for S=5/2.