Percolative, self-affine, and faceted domain growth in random three-dimensional magnets

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Abstract
We study the advance of an interface separating two magnetic domains in a three-dimensional random-field Ising model. An external magnetic field causes one domain to grow. Three types of growth are found. When disorder in the medium is large, the interface forms a self-similar pattern with large scale structure characteristic of percolation. As the disorder decreases, there is a critical transition to compact growth with a self-affine interface. Finally, for sufficiently weak disorder, simple faceted growth occurs. The transitions between these growth morphologies are related to results for bootstrap percolation. In the self-similar and self-affine growth regimes there are also critical transitions at the onset of steady-state motion. These are studied numerically, and found to lie in different universality classes. The critical exponents obtained from our simulations obey general scaling relations derived in the context of fluid invasion.