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.