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arXiv:cond-mat/9506111 · Physical Review Letters

Avalanches, Barkhausen Noise, and Plain Old Criticality

Olga Perković, Karin A. Dahmen, James P. Sethna

Published Dec 11, 1995• 305 citations
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Abstract

We explain Barkhausen noise in magnetic systems in terms of avalanches of domains near a plain old critical point in the hysteretic zero-temperature random-field Ising model. The avalanche size distribution has a universal scaling function, making nontrivial predictions of the shape of the distribution up to 50% above the critical point, where two decades of scaling are still observed. We simulate systems with up to ${1000}^{3}$ domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2D and $6\ensuremath{-}\ensuremath{\epsilon}$ predictions, and compare to a variety of experiments.

DOI
10.1103/physrevlett.75.4528

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We explain Barkhausen noise in magnetic systems in terms of avalanches of domains near a plain old critical point in the hysteretic zero-temperature random-field Ising model. The avalanche size distribution has a universal scaling function, making nontrivial predictions of the shape of the distribution up to 50% above the critical point, where two decades of scaling are still observed. We simulate systems with up to 10003{1000}^{3}10003 domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2D and 6\ensuremath−\ensuremathϵ6\ensuremath{-}\ensuremath{\epsilon}6\ensuremath−\ensuremathϵ predictions, and compare to a variety of experiments.
Abstract We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent close to 1.
Hysteresis loops are often seen in experiments at first-order phase transformations, when the system goes out of equilibrium. They may have a macroscopic jump (roughly as in the supercooling of liquids) or they may be smoothly varying (as seen in most magnets). We have studied the nonequilibrium zero-temperature random-field Ising-model as a model for hysteretic behavior at first-order phase transformations. As disorder is added, one finds a transition where the jump in the magnetization (corresponding to an infinite avalanche) decreases to zero. At this transition we find a diverging length scale, power-law distributions of noise (avalanches), and universal behavior. We expand the critical exponents about mean-field theory in 6-\ensuremath{\epsilon} dimensions. Using a mapping to the pure Ising model, we Borel sum the 6-\ensuremath{\epsilon} expansion to O(${\mathrm{\ensuremath{\epsilon}}}^{5}$) for the correlation length exponent. We have developed a method for directly calculating avalanche distribution exponents, which we perform to O(\ensuremath{\epsilon}). Our analytical predictions agree with numerical exponents in two, three, four, and five dimensions [Perkovi\ifmmode \acute{c}\else \'{c}\fi{} et al., Phys. Rev. Lett. 75, 4528 (1995)]. \textcopyright{} 1996 The American Physical Society.
Abstract We consider 2D random Ising ferromagnetic models, where quenched disorder is represented either by random local magnetic fields (random-field Ising model) or by a random distribution of interaction couplings (random-bond Ising model). In both cases, we first perform zero- and finite-temperature Monte Carlo simulations to determine how the critical temperature depends on the disorder parameter. We then focus on the reversal transition triggered by an external field and study the associated Barkhausen noise. Our main result is that the critical exponents characterizing the power law associated with the Barkhausen noise exhibit a temperature dependence in line with existing experimental observations.
Abstract We analyze the nonequilibrium athermal random field Ising model (RFIM) at equilateral cubic lattices of finite size L and show that the entire range of disorder consists of three distinct domains in which the model manifests different scaling behaviour. The first domain contains the values of disorder R that are below the critical disorder R c where the spanning avalanches almost surely appear when the system is driven by the external magnetic field. The spanning avalanches become unlikely for disorders above the size-dependent effective disorder R c eff ( L ) > R c , and the system response is size-independent. Between the foregoing two lies the domain of transitional disorders R c < R < R c eff ( L ) vanishing in the thermodynamic limit. In this domain, not recognized in the literature so far, all types of spanning avalanches exist, whereas for R < R c only the avalanches spanning all three dimensions are present. Like for R < R c the data collapsing is possible only for distributions having the same value of (1 − R c / R ) L 1/ ν , however with different universal scaling functions than in R < R c case; ν is the correlation length exponent. The foregoing findings follow from the extensive simulations of L ⩽ 2048 systems enabling us to propose modified values of some of the RFIM critical exponents and nonuniversal critical parameters as well as the analytic forms of universal scaling functions and different definitions of reduced magnetization and reduced magnetic field.
We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension ${d}_{DR}\ensuremath{\approx}5.1$. We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dDR{d}_{DR}dDR​, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.