Critical behavior of thin Ising films with noninteger thicknesses

We studied the ferromagnetic Ising model on thin films with two different local thickness distributions and noninteger mean thicknesses. In order to represent layer-by-layer growth, we considered films with a finite number I of complete layers and one randomly filled layer with probability x (mean thickness L=I+x). The T-c(L) curve is not smooth at integer values of L and, for L less than or similar to 5, it is remarkably different from the concave curve that interpolates the data for flat films (integer L). However, there is no evidence of a decrease of T-c for small x, in contrast to the oscillations of the mean coordination number. The critical exponents are the same of flat films. These results are obtained for three different ratios of the couplings inside the layers and between different layers. We also considered films with a Gaussian distribution of thicknesses of mean L and variance (Delta L)(2)/2, where Delta L=L/2, in order to represent the growth with increasing roughness. The T-c(L) curve is smooth and concave for continuous L. A quantitative difference from the scaling of T-c in flat films, for small thicknesses, is given by the shift exponent lambda in T-c(infinity)-T-c(L)similar to L-lambda. We discuss the relations of our results and the T-c(L) curves of some real magnetic films.