  We study Barkhausen noise in a diluted two-dimensional Ising model with the
extended domain wall and weak random fields occurring due to coarse graining.
We report two types of scaling behavior corresponding to (a) low disorder
regime where a single domain wall slips through a series of positions when the
external field is increased, and (b) large disorder regime, which is
characterized with nucleation of many domains. The effects of finite
concentration of nonmagnetic ions and variable driving rate on the scaling
exponents is discussed in both regimes. The universal scaling behavior at low
disorder is shown to belong to a class of critical dynamic systems, which are
described by a fixed point of the stochastic transport equation with
self-consistent disorder correlations.
