FINITE-SIZE-SCALING ON RANDOM MAGNETIC-STRUCTURES

The dependence of physical quantities on the finite size of a structur e and their dependence on the surface roughness are the questions cons idered in our studies of the ferromagnetic Ising model on two- and thr ee-dimensional systems. In two dimensions, we consider Very long strip s of random widths satisfying a Gaussian distribution with mean L and rms deviation Delta L. Finite-size scaling relations are satisfied onl y in lengths greater than in the corresponding uniform systems and the corrections increase with Delta L. In three dimensions, we consider t hin films with length and width N, one flat surface and the same distr ibutions of thicknesses (L, Delta L). The critical temperature decreas es for fixed L and increasing Delta L. The specific heat peaks of roug h films are reduced when compared to the uniform films, but the suscep tibility peaks are not. The finite-size scaling relations do not have remarkable changes when compared to the uniform firms, and the roughne ss patterns with Delta approximate to 1 become irrelevant for L approx imate to 15. The relations of our results and recent experiments in ma gnetic thin films are discussed. (C) 1998 Elsevier Science B.V. All ri ghts reserved.