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 $\mathrm{\Delta }$. Growth is driven by a uniform applied magnetic field, whose value is kept equal to the critical value $H_c(\mathrm{\Delta })$ for the onset of steady motion. Two growth regimes are clearly identified. For low $\mathrm{\Delta }$ the growing domain is compact, with a self-affine external interface. For large $\mathrm{\Delta }$ a self-similar percolation-like morphology is obtained. A multi-critical point at $({\mathrm{\Delta }}_c$, $H_c({\mathrm{\Delta }}_c))$ separates the two types of growth. We extract the critical exponents near ${\mathrm{\Delta }}_c$ 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 $H_c(\mathrm{\Delta })$.