Avalanche-size distribution at the depinning transition: A numerical test of the theory

avalanches, and ζ the roughness exponent at the depinning transition. Measurement of the scaling function f(s) := sp(s) is compared with the predictions from a recent Functional RG (FRG) calculation, both at mean-field and one-loop level. The avalanche-size exponent τ is found in good agreement with the conjecture τ = 2− 2/(d+ ζ), recently confirmed to one loop via the FRG. The function f(s) exhibits a shoulder and a stretched exponential decay at large s, ln f(s) ∼ −s, with δ ≈ 7/6 in d = 1. The function f(s), universal ratios of moments, and the generating function ̇ e ̧ are found in excellent agreement with the one-loop FRG predictions. The distribution of local avalanche sizes Sφ, i.e. of the jumps of a subspace of the manifold of dimension dφ, is also computed and compared to our FRG predictions, and to the conjecture τφ = 2− 2/(dφ + ζ).