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), body-centered cubic (BCC) and face-centered cubic (FCC) lattices with Gaussian, Uniform and Bimodal distributions for the disorder Delta. At small-r, the correlation function C (r, Delta) shows a cusp singularity characterised by a non-integer roughness exponent alpha signifying rough fractal interfaces with dimension d(f) = d - alpha. In the paramagnetic phase (Delta > Delta(c)), alpha similar or equal to 0.5 for all lattice and disorder types. In the ferromagnetic phase (Delta < Delta(c)), alpha similar or equal to 0.66 with minor variations for the different lattice types. Our predictions are confirmed by scattering data from diluted antiferromagnets (DAFFs). Fractal interfaces have important implications on growth and relaxation.