  We study numerically the coarsening dynamics of the Ising model on a regular
lattice with random bonds and on deterministic fractal substrates. We propose a
unifying interpretation of the phase-ordering processes based on two classes of
dynamical behaviors characterized by different growth-laws of the ordered
domains size - logarithmic or power-law respectively. It is conjectured that
the interplay between these dynamical classes is regulated by the same
topological feature which governs the presence or the absence of a
finite-temperature phase-transition.
