Fractal character of the phase ordering kinetics of a diluted ferromagnet

We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different properties at short or long distances. Specifically, on lengthscales larger than the typical domains' size the topology is that of critical random percolation, similarly to what observed in clean systems or models with different kinds of quenched disorder. On smaller lengthscales a dilution dependent fractal dimension emerges. The Hausdorff dimension increases with increasing dilution d up to the value 4/3 expected at the bond percolation threshold d  =  1/2. We discuss how such different geometries develop on different lengthscales during the phase-ordering process and how their simultaneous presence determines the scaling properties of observable quantities. (paper: classical statistical mechanics, equilibrium and non-equilibrium)