Scaling of critical self-organized magnetic-domain formations

We report a numerical investigation of scaling laws obeyed by the response of a domain wall separating regions of opposite magnetization in a recording tape. The universality of the ${\mathit{t}}^{\mathrm{-}1.1}$ power law for the resettlement time of the pattern following a disturbance breaks down for large t. The scaling law for large t depends on anisotropy (i.e., inclination of the wall to the tape direction) and tape length. For infinite tape length, the remaining dependence of the power law on anisotropy is best fitted by Widom scaling. We also find that a critical self-organized state is attained whether or not successive steps of the algorithm involve random elements, as long as the initial state is random.