Statistics of static avalanches in a random pinning landscape

Abstract

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 epsilon=4-d expansion from a tree and 1-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 the Burgers equation and to dynamic avalanches are discussed.

4 pages, 5 figures

References in corpus (3)

• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition
• Pair correlations in sandpile model: a check of logarithmic conformal field theory

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