We report extensive measurements, with sufficiently large statistics, of the Barkhausen noise ͑BN͒ in the case of the commercial VITROVAC 6025 X metal glass sample. Applying a very scrutinized numerical procedure, we have extracted over one million of the BN elementary signals from the raw experimental data, whereby we made a rather precise estimation of the relevant power law exponents. In conjunction with the experimental part of the work, we have recognized a generic shape of a single BN elementary signal ͑BNES͒, and we have put forward, without invoking any existing model of BN, a simple mathematical expression for BNES. Using the proposed expression for BNES in a statistical analysis, we have been able to predict scaling relations and an elaborate formula for the power spectrum. We have also obtained these predictions within the generalized homogeneous function approach to the BNES's probability distribution function, which we have substantiated by the corresponding data collapsing analysis. Finally, we compare all our findings with results obtained within the current experimental and theoretical research of BN. ͓S1063-651X͑96͒13409-7͔

We give numerical evidence that the two-dimensional nonequilibrium zero-temperature random field Ising model exhibits critical behavior. Our findings are based on the results of scaling analysis and collapsing of data, obtained in extensive simulations of systems with sizes sufficiently large to clearly display the critical behavior.

We present in detail the scaling analysis and data collapse of avalanche distributions and joint distributions that characterize the recently evidenced critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model. The distributions are collected in extensive simulations of systems with linear sizes up to L=131072.

The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the time-scale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the two-dimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.