### A direct measurement of the renormalized disorder correlator, and
avalanche size distributions

Kay Wiese, ENS Paris

The central object of the field theory of disordered systems is the
renormalized disorder correlator. Due to metastability in the system,
it has a cusp at the origin. From a field-theory point of view, this
cusp questions the method as such. It is therefore important to
measure it directly, in a numerical simulation or experiment. However,
only recently such a protocol has been devised. Here we present
numerical simulations and the first experiment to implement this
protocol: We measure the center-of-mass fluctuations of the height of
a contact line at depinning, including the cusp.
This cusp is also the key to obtain the avalanche-size distribution
directly from the field theory. This is the first analytic method
(apart from few exact results) to go beyond mean field, allowing to
predict the whole scaling function: the critical behavior at small
avalanche sizes, characterized by the exponent tau, the shoulder at
intermediate sizes, and a compacted exponential tail. These results
are confronted with large-scale numerical simulations.