Structure factor for dilute magnetic systems

The structure factor of dilute magnetic systems in the ordered phase contains, in addition to the usual q-dependent susceptibility, another term, which results from the fluctuations in the local quenched magnetic moments. This term, first considered by Grinstein, Ma, and Mazenko (GMM), is discussed here using scaling arguments, and calculated explicitly in d=4- and d=2+ dimensions, as well as for an infinite number of spin components, n. Contrary to the earlier calculation by GMM, this term is shown to have no coexistence singularities when n 2. In the Ising case, this term combines with the usual susceptibility term to affect the measured critical amplitude ratios: The measured amplitude of the structure factor below Tc is not equal to that calculated for the susceptibility, as previously assumed.