Faceting via correlated disorder of a stochastically growing interface or domain boundary
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We consider a stochastically growing or evaporating interface in the presence of disorder which is correlated in the direction normal to the interface. The growth or evaporation rate at randomly distributed disorder points is assumed to be different from that of the rest of the interface. This model is of relevance not only to island growth in overlayers, but also to the domain growth in an ultrathin magnetic film after reversal of the magnetization. For a growing one-dimensional interface or a moving domain wall in a magnetic film on a crystal surface, this type of correlated disorder simulates the effect of, e.g., surface steps or grain boundaries on the growth process while, for a growing or evaporating crystal surface, it describes the effect of screw dislocations or of grain boundaries again. We show that, for interface dimensions d = 1,2 during the growth (or evaporation) e-scale faceting develops, although on a small scale the interface is rough. Exploiting the formal connection between the interface model and the model used in the problem of flux line localization in a superconductor we show that correlated disorder localizes the flux line in the presence of point disorder.