  We discuss a model metallic glass in which Barkhausen Noise can be studied in
exquisite detail, free of thermal effects and of the rate of ramping of the
magnetic field. The mechanism of the jumps in magnetic moment that cause the
Barkhausen Noise can be fully understood as consecutive instabilities where an
eigenvalue of the Hessian matrix hits zero, leading to a magnetization jump
$\Delta m$ which is simultaneous with a stress and energy changes $\Delta
\sigma$ and $\Delta U$ respectively. Contrary to common belief we find no
"movements of magnetic domain boundaries" across pinning sites, no fractal
domains, no self-organized criticality and no exact scaling behaviour. We
present a careful numerical analysis of the statistical properties of the
phenomenon, and show that with every care taken this analysis is tricky, and
easily misleading. Without a guiding theory it is almost impossible to get the
right answer for the statistics of Barkhausen Noise. We therefore present an
analytic theory, showing that the probability distribution function (pdf) of
Barkhausen Noise is not a power law times an exponential cutoff.
