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

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

2010-07-13

arxiv.org/abs/1007.2069v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 1 figure

Scientific paper

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 rho(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 rho(S) ~ 1/(S)^tau with exponent tau=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, rho(S) ~ S exp(-A S^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.

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