Diffusion and spin correlation in fractal percolation clusters

We have performed Monte Carlo simulations and theoretical calculations of the time decay behavior of the dipolar and spin exchange autocorrelation functions $G_N$(τ) over a range of concentrations p (0<p<1) of randomly diluted magnetic species diffusing in a lattice. For p below the percolation threshold $p_c$, $G_N$(τ) decays exponentially, at long time, with an effective time constant τ(p) increasing with the concentration. We show that this result is characteristic of a bounded diffusion in a single average cluster explored in the average time 〈τ(p)〉.