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

TL;DR

This paper derives a universal formula for the size distribution of avalanches in mean-field glasses, revealing power-law behavior in spin-glasses and connections to Barkhausen noise and turbulence.

Contribution

It provides a general theoretical framework for avalanche size distributions in mean-field models with replica symmetry breaking, including new power-law results.

Findings

Power-law distribution rho(S) ~ 1/S in SK spin-glass

Exponential decay rho(S) ~ S exp(-A S^2) in one-step solutions

Connections established between avalanches, Barkhausen noise, and turbulence

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 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.