Random Field Ising Models: Fractal Interfaces and their Implications

We use a computationally efficient graph-cut (GC) method to obtain exact ground-states of the d = 3 random field Ising model (RFIM) on simple cubic (SC), bodycentered cubic (BCC) and face-centered cubic (FCC) lattices with Gaussian, Uniform and Bimodal distributions for the disorder Δ. At small- r , the correlation function C ( r ; Δ) shows a cusp singularity characterised by a non-integer roughness exponent α signifying rough fractal interfaces with dimension d _f= d – α . In the paramagnetic phase (Δ > Δ _c ), α ≃ 0:5 for all lattice and disorder types. In the ferromagnetic phase (Δ < Δ _c ), α ≃ 0:66 with minor variations for the diαerent lattice types. Our predictions are conformed by scattering data from diluted antiferromagnets (DAFFs). Fractal interfaces have important implications on growth and relaxation. (paper)