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.
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