Spin wave theory of dilute one-dimensional magnets

The low-temperature specific heat and inelastic neutron scattering from dilute one-dimensional Heisenberg magnets are computed using spin wave theory. The specific heat and inelastic neutron scattering are calculated exactly for segments of finite length and the properties for the random systems are computed by summing over segments. Analytical results in the limit of very low temperature for the specific heat are obtained for both ferromagnetic and antiferromagnetic systems. The results for the inelastic neutron scattering law are very similar to those obtained previously by computer simulation.