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

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(Δ M ) of the sizes of magnetization jumps Δ M along the equilibrium magnetization curve at zero temperature. Continuous RSB allows for a power-law behavior ρ(Δ M )∼1/(Δ M ) 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 − AS 2 . 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.