  We consider the three-dimensional randomly diluted Ising model and study the
critical behavior of the static and dynamic spin-spin correlation functions
(static and dynamic structure factors) at the paramagnetic-ferromagnetic
transition in the high-temperature phase. We consider a purely relaxational
dynamics without conservation laws, the so-called model A. We present Monte
Carlo simulations and perturbative field-theoretical calculations. While the
critical behavior of the static structure factor is quite similar to that
occurring in pure Ising systems, the dynamic structure factor shows a
substantially different critical behavior. In particular, the dynamic
correlation function shows a large-time decay rate which is momentum
independent. This effect is not related to the presence of the Griffiths tail,
which is expected to be irrelevant in the critical limit, but rather to the
breaking of translational invariance, which occurs for any sample and which, at
the critical point, is not recovered even after the disorder average.
