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

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.

6 pages, 1 figure

References in corpus (9)

• Burgers Turbulence
• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• Mean field theory for the three-dimensional Coulomb glass
• Behavior of Ising Spin Glasses in a Magnetic Field
• Unexpected universality in static and dynamic avalanches
• Potts Glass on Random Graphs
• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Universality class of replica symmetry breaking, scaling behavior, and the low-temperature fixed-point order function of the Sherrington-Kirkpatrick model
• Noise Measurement of Interacting Ferromagnetic Particles with High Resolution Hall Microprobes

Cited by in corpus (36)

• Fractal free energy landscapes in structural glasses
• Marginal Stability in Structural, Spin and Electron Glasses
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• Exact theory of dense amorphous hard spheres in high dimension. III. The full RSB solution
• The simplest model of jamming
• May's Instability in Large Economies
• Replica theory of the rigidity of structural glasses
• Avalanche dynamics of elastic interfaces
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Avalanche shape and exponents beyond mean-field theory
• Quantum charge glasses of itinerant fermions with cavity-mediated long-range interactions
• Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution
• First-principle derivation of static avalanche-size distribution
• Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
• Dynamics and Correlations among Soft Excitations in Marginally Stable Glasses
• Hessian spectrum at the global minimum of high-dimensional random landscapes
• Self-Organized Criticality in Glassy Spin Systems Requires a Diverging Number of Neighbors
• Origin of scale-free intermittency in structural first-order phase transitions
• Spherical spin glass model with external field
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• Seismic-like organization of avalanches in a driven long-range elastic string as a paradigm of brittle cracks
• Surfing on minima of isostatic landscapes: avalanches and unjamming transition
• Functional renormalization-group approach to decaying turbulence
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches
• Self-Organized Criticality as Witten-type Topological Field Theory with Spontaneously Broken Becchi-Rouet-Stora-Tyutin Symmetry
• Atomistic Simulations of Magnetic Amorphous Solids: Magnetostriction, Barkhausen noise and novel singularities
• Chaos properties of the one-dimensional long-range Ising spin-glass
• Exact numerical solution of the fully-connected classical and quantum Heisenberg spin glass
• Shock statistics in higher-dimensional Burgers turbulence
• Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses
• Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations
• Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm
• Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimum
• Numerical renormalization of glassy dynamics
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Fragmented perspective of self-organized criticality and disorder in log gravity