Finite-size scaling on random magnetic structures

We study the ferromagnetic Ising model on very long strips of random widths using transfer matrix techniques. The width distribution is Gaussian with mean L and rms deviation ΔL, which may be constant for any L (type I) or proportional to L (type II). We calculate the initial susceptibility for strips with 4⩽L⩽12, obtaining estimates of the ratio of exponents (γ/ν)_L and the pseudocritical temperature T^*(L,L-1). In strips of type I, those estimates satisfy finite-size scaling, with finite-size corrections increasing with ΔL, and in strips of type II it is satisfied only for very large lengths L. We discuss the influence of nonuniform thicknesses on the magnetism of low-dimensional systems, comparing the finite-size corrections of this problem to those which fit the experimental data of magnetic thin films.