Abstract
A model of randomly diluted ferromagnets with local random fields exhibiting Barkhausen noise when slowly driven by the external field and a cellular automaton with quenched random bonds are studied by numerical simulations. The defect cellular automaton maintains critical steady states in the mean-field universality class for all strengths of disorder and conservative dynamics. In the disordered ferromagnet, the scaling properties of Barkhausen noise resembling self-organized criticality are found in the region of moderate disorder with scaling exponents depending on both the concentration of defect sites and driving rate. The transport properties and the disorder-induced phase transition are discussed.