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 L and rms deviation ΔL. Finite-size scaling relations are satisfied only in lengths greater than in the corresponding uniform systems and the corrections increase with ΔL. In three dimensions, we consider thin films with length and width N, one flat surface and the same distributions of thicknesses (L,ΔL). The critical temperature decreases for fixed L and increasing ΔL. 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 ΔL≈1 become irrelevant for L≈15. The relations of our results and recent experiments in magnetic thin films are discussed.
