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.
The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and sca…
Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we go beyond power laws and focus on the multifractal scenario to quantify the temporal scaling character…
The demagnetization curve, or initial magnetization curve, is studied by examining the embedded Barkhausen noise using the non-equilibrium, zero temperature random-field Ising model. The demagnetization curve is found to reflect the critical point seen as the system's disorder is changed. Critical scaling is found for avalanche sizes and the size and number of spanning avalanches. The critical exponents are derived from those related to the saturation loop and subloops. Finally, the behavior in the presence of long range demagnetizing fields is discussed. Results are presented for simulations …
Many systems crackle, from earthquakes and financial market to Barkhausen effect in ferromagnetic materials. Despite the diversity in essence, the noise emitted in these dynamical systems consists of avalanche-like events with broad range of sizes and durations, characterized by power-law avalanche distributions and typical average avalanche shape that are signatures dependent on the universality class of the underlying dynamics. Here we focus on the crackling noise in ferromagnets and scrutinize the traditional statistics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic…
We show that Barkhausen noise in two-dimensional disordered ferromagnets with extended domain walls is characterized by the avalanche size exponent $τ_s =1.54$ at low disorder. With increasing disorder the characteristic domain size is reduced relative to the system size due to nucleation of new domains and a dynamic phase transition occurs to the scaling behavior with $τ_s=1.30$. The exponents decrease at finite driving rate. The results agree with recently observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied anisotropic stress is varied.
In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the non-equilibrium zero temperature Random Field Ising Model (RFIM), we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents $τ$ and $1/σνz$ in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling funct…
We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation, and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhause…
With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed…
The field-driven magnetisation reversal processes in disordered systems exhibit a collective behaviour that is manifested in the scale-invariance of avalanches, closely related to underlying dynamical mechanisms. Using the multifractal time series analysis, we study the structure of fluctuations at different scales in the accompanying Barkhausen noise. The stochastic signal represents the magnetisation discontinuities along the hysteresis loop of a 3-dimensional random field Ising model simulated for varied disorder strength and driving rates. The analysis of the spectrum of the generalised Hu…
Experimental investigations of the scaling behavior of Barkhausen avalanches in out-of-plane ferromagnetic films yield widely different results for the values of the critical exponents despite similar labyrinthine domain structures, suggesting that universality may not hold for this class of materials. Analyzing a phase field model for magnetic reversal, we show that avalanche scaling is bounded by characteristic lengthscales arising from the competition between dipolar forces and exchange interactions. We compare our results with the experiments and find a good qualitative and quantitative ag…
We investigate the statistical properties of the Barkhausen noise in amorphous ferromagnetic films with thicknesses in the range between $100$ and $1000$ nm. From Barkhausen noise time series measured with the traditional inductive technique, we perform a wide statistical analysis and establish the scaling exponents $τ$, $α$, $1/σνz$, and $\vartheta$. We also focus on the average shape of the avalanches, which gives further indications on the domain wall dynamics. Based on experimental results, we group the amorphous films in a single universality class, characterized by scaling exponents $τ\s…
We investigate the dimensional crossover of scaling properties of avalanches (domain-wall jumps) in a single-interface model, used for the description of Barkhausen noise in disordered magnets. By varying the transverse aspect ratio $A=L_y/L_x$ of simulated samples, the system dimensionality changes from two to three. We find that perturbing away from $d=2$ is a relevant field. The exponent $τ$ characterizing the power-law scaling of avalanche distributions varies between $1.06(1)$ for $d=2$ and $1.275(15)$ for $d=3$, according to a crossover function $f(x)$, $x \equiv (L_x^{-1})^ϕ/A$, with $ϕ…
Antiferromagnetic Barkhausen noise induced by weak random-field disorder
Jožef Stefan Institute（约热·斯特凡研究所）；Complexity Science Hub（复杂科学中心）；Institute of Physics, Pregrevica 118, 11080 Belgrade, Serbia（塞尔维亚贝尔格莱德普雷格雷维察街118号物理研究所）
Many systems respond to slowly changing external conditions with crackling noise, created by avalanches or pulses of a broad range of sizes. Examples range from Barkhausen Noise in magnets to earthquakes. Here we discuss how the scaling behavior of the avalanche size and duration distribution and the power spectra of this noise depend on the rate at which the external conditionsare changed. We derive an exponent inequality as a criteria for the relevance of adding a small driving rate to the adiabatic model. We use the zero temperature nonequilibrium random field Ising model to test our result…
We discuss the application of wavelet transforms to a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of surface tension), the effective interface roughness exponent $ζ$ is $\simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times betw…
We study the zero-temperature relaxation dynamics of an electron glass model with single-electron hops. We find numerically that in the charge rearrangements (avalanches) triggered by displacing an electron, the number of electron hops has a scale-free, power-law distribution up to a cutoff diverging with the system size $N$, independently of the disorder strength and provided hops of arbitrary length are allowed. In avalanches triggered by the injection of an extra electron, the distribution does not have a power-law limit, but its mean diverges non-trivially with $N$. In both cases, the aval…
We study avalanches along the hysteresis loop of long-range interacting spin-glasses with continuous XY-symmetry - which serves as a toy model of granular superconductors with long-range and frustrated Josephson couplings. We identify sudden jumps in the $T=0$ configurations of the XY-phases, as an external field is increased. They are initiated by the softest mode of the inverse susceptibility matrix becoming unstable, which induces an avalanche of phase updates (or spin alignments). We analyze the statistics of these events, and study the correlation between the non-linear avalanches and the…
We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model had been used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with non-trivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay $\sim ω^{-t}$, with $t<2$ for finite driving rates, revealing the influence of the internal s…
For a long time, it has been known that the power spectrum of Barkhausen noise had a power-law decay at high frequencies. Up to now, the theoretical predictions for this decay have been incorrect, or have only applied to a small set of models. In this paper, we describe a careful derivation of the power spectrum exponent in avalanche models, and in particular, in variations of the zero-temperature random-field Ising model. We find that the naive exponent, (3-tau)/(sigma nu z), which has been derived in several other papers, is in general incorrect for small tau, when large avalanches are commo…
We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density rho(Delta M) of the magnetization jumps Delta M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that rho(Delta M) ~ (Delta M)^(-tau) with an avalanche exponent tau=1 for the SK model, originating from the marginal stabil…
In this chapter, we discuss avalanches in glasses and disordered systems, and the macroscopic dynamical behavior that they mediate. We briefly review three classes of systems where avalanches are observed: depinning transition of disordered interfaces, yielding of amorphous materials, and the jamming transition. Without extensive formalism, we discuss results gleaned from theoretical approaches -- mean-field theory, scaling and exponent relations, the renormalization group, and a few results from replica theory. We focus both on the remarkably sophisticated physics of avalanches and on relativ…
We probe the droplet excitations in short range spin glasses by adding a perturbative long range interaction that decays with distance as a power law: $J/r^σ$. It is shown that if the power law exponent $σ$ is smaller than the spatial dimension $d$, the perturbation induces large scale avalanches which roll until they force the system to develop a pseudo gap in the excitation spectrum of the stabilities. This makes the perturbative long range interactions relevant for $σ< σ_c = d$. The droplet theory predicts that the critical exponent $σ_c$ depends on the droplet stiffness exponent as $σ_c=d-…
We report the measurement of multivariable scaling functions for the temporal average shape of Barkhausen noise avalanches, and show that they are consistent with the predictions of simple mean-field theories. We bypass the confounding factors of time-retarded interactions (eddy currents) by measuring thin permal- loy films, and bypass thresholding effects and amplifier distortions by applying Wiener deconvolution. We find experimental shapes that are approximately symmetric, and track the evolution of the scaling function. We solve a mean- field theory for the magnetization dynamics and calcu…
We explore the stability of far-from-equilibrium metastable states of a three-dimensional Coulomb glass at zero temperature by studying charge avalanches triggered by a slowly varying external electric field. Surprisingly, we identify a sharply defined dynamical ("depinning") phase transition from stationary to nonstationary charge displacement at a critical value of the external electric field. Using particle-conserving dynamics, scale-free system-spanning avalanches are observed only at the critical field. We show that the qualitative features of this depinning transition are completely diff…
In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena considered. I focus specifically on elastic interfaces in random media, such as pinned domain walls in ferromagnets containing defects, fluid contact lines on rough surfaces, etc. The goal is to understand static properties (e.g. the roughness) of such systems, and their dynamics in response to an external force. The interface moves in avalanches, triggered at ra…
Barkhausen noise as found in magnets is studied both with and without the presence of long-range (LR) demagnetizing fields using the non-equilibrium, zero-temperature random-field Ising model. Two distinct subloop behaviors arise and are shown to be in qualitative agreement with experiments on thin film magnets and soft ferromagnets. With LR fields present subloops resemble a self-organized critical system, while their absence results in subloops that reflect the critical point seen in the saturation loop as the system disorder is changed. In the former case, power law distributions of noise a…
Despite the extreme simplicity in their definition, spin glasses disclose a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis we try to shed light on some of them, focusing on one hand on the search of phase transitions under perturbations of the Hamiltonian, and on the other hand on the zero-temperature properties and responses to external stimuli. After introducing spin glasses through a historiographical review, and useful concepts on phase transitions and numerics, the results of two massive Monte Carlo campaigns on three-dimensional systems are shown.…
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for al…
We use record dynamics (RD), a coarse-grained description of the ubiquitous relaxation phenomenology known as "aging", as a diagnostic tool to find universal features that distinguish between the energy landscapes of Ising spin models and the ferromagnet. According to RD, a non-equilibrium system after a quench relies on fluctuations that randomly generate a sequence of irreversible record-sized events (quakes or avalanches) that allow the system to escape ever-higher barriers of meta-stable states within a complex, hierarchical energy landscape. Once these record events allow the system to ov…
Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here we study quantum dynamics of an isolated 1d spin-glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via resonance avalanche mechanism, that is also responsible for the destruction of MBL in non-glassy systems with power-law interactions. At low energy densities, the interaction-induced fi…
