An Ising model with ferromagnetically coupled, randomly distributed impurities in a linear antiferromagnetic chain was previously presented to interpret the magnetization of certain organic free radicals. Simple assumptions permit this model to be generalized to other anisotropies. It is shown that for a small concentration of impurities there are two contributions to the low-temperature magnetization. One is a local contribution and is proportional to the number of impurities, q. It is largest and least localized for Heisenberg coupling. The other contribution is nonlocal, depends upon the zero-temperature long-range order ω, and probably can be represented as a single spin of magnitude gβ(ωq)122. Near the Ising limit the system acts like a superparamagnet. The magnetic-field dependence of the magnetization can be used to separate the two contributions. For Heisenberg coupling the magnetization will be paramagnetic and this paramagnetism persists as kT|J|→0. This prediction requires ω=0 and hence provides a direct test of this relation. The low-temperature experimental results on the free radicals agree with the paramagnetism predicted in the case of Heisenberg coupling. © 1967 The American Physical Society.