By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.
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