We simulate Barkhausen avalanches on fractal clusters in a two-dimensional diluted Ising ferromagnet with an effective Gaussian random field. We vary the concentration of defect sites $c$ and find a scaling region for moderate disorder, where the distribution of avalanche sizes has the form $D(s,c,L){=s}^{-[1+\tau (c\left)\right]}D\left({\mathrm{sL}}^{{-D}_s\left(c\right)}\right)$. The exponents $\tau \left(c\right)$ for size and $\alpha \left(c\right)$ for length distribution, and the fractal dimension of avalanches $D_s\left(c\right)$, satisfy the scaling relation $D_s\left(c\right)\tau \left(c\right)=\alpha \left(c\right)$. For fixed disorder the exponents vary with driving rate in agreement with experiments on amorphous Si-Fe alloys.

• Received 16 May 1996

DOI:https://doi.org/10.1103/PhysRevLett.77.3843