Statistics of static avalanches in a random pinning landscape

Pierre Le Doussal, Arthur Alan Middleton, Kay Jörg Wiese

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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 Iμ=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.

Original languageEnglish (US)
Article number050101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume79
Issue number5
DOIs
StatePublished - May 7 2009

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ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

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