Magnetism of thin Ising films with rough surfaces

We study the ferromagnetic Ising model on thin films of random thicknesses using Monte Carlo simulations. The films have a simple cubic lattice structure, length and width N, one flat surface and discretized Gaussian distributions of thicknesses with mean L and rms deviation ΔL. We consider the cases of ΔL=const for any L (type I) and ΔL/L=const for any L (type II). A decrease of the critical temperature T_c(L,ΔL) for fixed L and increasing roughness (ΔL) is observed. The specific-heat peak of rough films of finite length is reduced when compared to the uniform films. The susceptibility peak is not reduced for small roughness (ΔL<~1), and decreases for larger roughness. This type of disorder is shown to be irrelevant for the critical exponents, and two-dimensional finite-size scaling relations (in the lateral length N) do not have remarkable corrections when compared to the uniform films. In films of type I, the critical temperature shift t_L=T_c(3D)-T_c(L,ΔL) scales with L approximately as in the uniform films, and a small roughness becomes irrelevant for L>10, where three-dimensional scaling is attained. In films of type II, t_L decreases slowly with L, in disagreement with both two- and three-dimensional behavior for L<~10. We discuss the possible connections of our results and experiments in magnetic thin films.