Statistics of static avalanches in a random pinning landscape

TL;DR

This paper analyzes the statistical properties of static avalanches in a disordered elastic interface, deriving analytical distributions and comparing them with numerical simulations across different dimensions.

Contribution

It provides the first analytical derivation of avalanche size distributions in a random pinning landscape using functional renormalization and compares results with numerical data.

Findings

Analytical avalanche size distribution obtained via epsilon expansion.

Good agreement between theory and numerical simulations in 2D and 3D.

Connections established between static avalanches, Burgers equation, and dynamic avalanches.

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.