Ground-state morphologies in the random-field Ising model: Scaling properties and non-Porod behavior

We use a computationally efficient graph-cut method (GCM) to obtain the ground-state morphologies (at zero temperature) of the random-field Ising model in d = 2,3. The GCM enables us to obtain comprehensive numerical results on large-scale systems. We analyze the morphologies by computing correlation functions and structure factors. These quantities enable us to precisely evaluate characteristic properties, e.g., domain sizes, scaling functions, roughness exponents, fractal dimensions, etc.