Avalanches in mean-field models and the Barkhausen noise in spin-glasses

¹ CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75005 Paris, France, EU
² The Abdus Salam International Center for Theoretical Physics - Strada Costiera 11, 34151 Trieste, Italy, EU

^a markusm@ictp.it

Received: 13 July 2010
Accepted: 20 August 2010

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 (RSB) saddle points. For the Sherrington-Kirkpatrick (SK) spin-glass it yields the density ρ(ΔM) of the sizes of magnetization jumps ΔM along the equilibrium magnetization curve at zero temperature. Continuous RSB allows for a power-law behavior ρ(ΔM)∼1/(ΔM)^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 1-step solution, ρ(S)∼Se^−AS2. 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.