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 hat surface and discretized Gaussian distributions of thicknesses with mean L and rms deviation Delta L. We consider the cases of Delta L = Const for any L (type I) and Delta L/L = const for any L (type II). A decrease of the critical temperature T-c(L, Delta L) for fixed L and increasing roughness (Delta L) 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 fur small roughness (Delta L less than or equal to 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 tin 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, Delta L) 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 less than or equal to 10. We discuss the possible connections of our results and experiments in magnetic thin films. [S0163-1829(98)01922-5].