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