Morphology transitions in three-dimensional domain growth with Gaussian   random fields
  We study the morphology of magnetic domain growth in disordered three dimensional magnets. The disordered magnetic material is described within the random-field Ising model with a Gaussian distribution of local fields with width $\Delta$. Growth is driven by a uniform applied magnetic field, whose value is kept equal to the critical value $H_c(\Delta)$ for the onset of steady motion. Two growth regimes are clearly identified. For low $\Delta$ the growing domain is compact, with a self-affine external interface. For large $\Delta$ a self-similar percolation-like morphology is obtained. A multi-critical point at $(\Delta_c$, $H_c(\Delta_c))$ separates the two types of growth. We extract the critical exponents near $\Delta_c$ using finite-size scaling of different morphological attributes of the external domain interface. We conjecture that the critical disorder width also corresponds to a maximum in $H_c(\Delta)$. 
Belita Koiller and Mark O. Robbins