Statistics of static avalanches in a random pinning landscape

We study the minimum-energy configuration of a d-dimensional elastic interface in a random potential tied to a harmonic spring. As a function of the spring position, the center of mass of the interface changes in discrete jumps, also called shocks or “static avalanches.” We obtain analytically the distribution of avalanche sizes and its cumulants within an ϵ=4−d expansion from a tree and one-loop resummation using functional renormalization. This is compared with exact numerical minimizations of interface energies for random-field disorder in d=2,3. Connections to dynamic avalanches are mentioned.