Statistics of static avalanches in a random pinning landscape
Pierre Le Doussal1, A. Alan Middleton2, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France
2Physics Department, Syracuse University, Syracuse NY 13244, USA
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 ε = 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.
arXiv:0803.1142 [pdf]
Phys. Rev. E 79 (2009) 050101 (R) [pdf]
Copyright (C) by Kay Wiese. Last edited March 17, 2008.