  We present a proof of principle for the validity of the functional
renormalization group, by measuring the force correlations in Barkhausen-noise
experiments. Our samples are soft ferromagnets in two distinct universality
classes, differing in the range of spin interactions, and the effects of eddy
currents. We show that the force correlations have a universal form predicted
by the functional renormalization group, distinct for short-range and
long-range elasticity, and mostly independent of eddy currents. In all cases
correlations grow linearly at small distances, as in mean-field models, but in
contrast to the latter are bounded at large distances. As a consequence,
avalanches are anti-correlated. We derive bounds for these anti-correlations,
which are saturated in the experiments, showing that the multiple domain walls
in our samples effectively behave as a single wall.
