Finite-size scaling on random magnetic structures

The dependence of physical quantities on the finite size of a structure and their dependence on the surface roughness are the questions considered in our studies of the ferromagnetic Ising model on two- and three-dimensional systems. In two dimensions, we consider very long strips of random widths satisfying a Gaussian distribution with mean and rms deviation . Finite-size scaling relations are satisfied only in lengths greater than in the corresponding uniform systems and the corrections increase with . In three dimensions, we consider thin films with length and width , one flat surface and the same distributions of thicknesses ( ). The critical temperature decreases for fixed and increasing . The specific heat peaks of rough films are reduced when compared to the uniform films, but the susceptibility peaks are not. The finite-size scaling relations do not have remarkable changes when compared to the uniform films, and the roughness patterns with become irrelevant for . The relations of our results and recent experiments in magnetic thin films are discussed.