Transition from compact to self-similar growth in disordered systems: Fluid invasion and magnetic-domain growth

Abstract

We consider the advance of the interface separating two domains in a random two-dimensional medium. The domains correspond to regions of opposite spin in magnetic systems or different fluid phases in fluid invasion. A driving force normal to the interface, corresponding to an external magnetic field or pressure, causes one domain to grow. Various types of disorder corresponding to random fields or bonds were studied. When disorder in the medium is large, the interface forms a fractal pattern with large-scale structure characteristic of percolation. As the disorder decreases, a transition to compact, faceted growth is observed if the distribution of random fields or bonds is bounded. The critical phenomena associated with this transition and its relation to a transition found in fluid invasion are discussed.