Numerical calculation of the functional renormalization group fixed-point functions at the depinning transition

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasistatically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows one to obtain the functional renormalization group (FRG) functions at the depinning transition. Following this procedure we are able to directly test the main predictions of FRG calculations. In particular, the universal form of the second cumulant Δ(u) is found to have a linear cusp at the origin, to be identical for RBs and RFs, different from the statics and in good agreement with two-loop FRG calculations. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG functions.