Avalanches in mean-field models and the Barkhausen noise in spin-glasses
Pierre Le Doussal1, Markus Müller2, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France,
2The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.
Abstract
We obtain a general formula for the distribution of sizes of "static avalanches", or shocks, in generic mean-field glasses with replica-symmetry-breaking saddle points. For the Sherrington-Kirkpatrick (SK) spin-glass it yields the density ρ(S) of the sizes of magnetization jumps S along the equilibrium magnetization curve at zero temperature. Continuous replica-symmetry breaking allows for a power-law behavior ρ(S) ~ S-τ with exponent τ = 1 for SK, related to the criticality (marginal stability) of the spin-glass phase. All scales of the ultrametric phase space are implicated in jump events. Similar results are obtained for the sizes S of static jumps of pinned elastic systems, or of shocks in Burgers turbulence in large dimension. In all cases with a one-step solution, ρ(S) ~ S exp(-A S2). A simple interpretation relating droplets to shocks, and a scaling theory for the equilibrium analog of Barkhausen noise in finite-dimensional spin glasses are discussed.
arXiv:1007.2069 [pdf]
EPL, 91 (2010) 57004 [pdf]
Copyright (C) by Kay Wiese. Last edited July 14, 2010.