Analytical expressions for Barkhausen jump size distributions

In previous calculations of Barkhausen jump size distributions, the Langevin equation was used to describe the pinning held h_c. In this paper, h_c is modeled by discretized random walks which are used to obtain analytical expressions for the Barkhausen jump size distribution, P(τ). For a bounded random walk which reduces to the Langevin function in the continuum limit, P(τ) is a sum of exponentials which is compared to functions of the form P(τ)=τ^-αexp(-τ/τ0). The scaling exponent changes from α≃1.5 for small jumps to α≃1.0 for jumps larger than the correlation length. For an unbounded random walk with exponentially distributed distances between steps in h_c, P(τ) is shown to be proportional to a modified Bessel function which, for long jumps, is asymptotically a pure power law, τ^-3/2. This suggests that the scaling exponent shift and the exponential cutoff are caused by correlations in h_c