Effects of interface width scaling and spatial correlations on Ising systems with rough boundaries

摘要

We studied the ferromagnetic Ising model on two-dimensional systems with rough boundaries and several thickness distributions. First, we considered very long strips with discretized Gaussian distributions of widths with mean 3 less than or equal to L less than or equal to 12. Systems with fixed interface width W and with increasing roughness (W similar to L-beta, with 0 less than or equal to beta less than or equal to 1) were analysed. We also considered strips with columns' heights correlations, where the difference in the heights of neighbouring columns was 0 or 1, with 0 less than or equal to beta less than or similar to 0.5. Free energies per spin, f(L), and initial susceptibilities, chi (L), were calculated using transfer matrix techniques at the critical temperature of the two-dimensional Ising model. The scaling of SL and of the finite-size estimates of the ratio of exponents (y/v)(L) was analysed. In systems with small and slowly increasing W (beta < 0.2), correlated or not, extrapolations of f(L). and (y/v)(L), to L --> infinity give accurate estimates of the critical parameters f(infinity) and y/v. In systems with rapidly increasing roughness, the deviations of those estimates from the exact values indicate the presence of large corrections in finite-size scaling relations. The comparison of systems with nearly the same beta shows that spatial correlations have no systematic effect on corrections to scaling. It suggests the reliability of uncorrelated models or related approximate systems for the description of scaling properties of thin magnetic films and other low-dimensional structures. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 23]