Hysteresis, Avalanches, and Noise: Numerical Methods

Abstract

In studying the avalanches and noise in a model of hysteresis loops we have developed two relatively straightforward algorithms which have allowed us to study large systems efficiently. Our model is the random-field Ising model at zero temperature, with deterministic albeit random dynamics. The first algorithm, implemented using sorted lists, scales in computer time as O(N log N), and asymptotically uses N (sizeof(double)+ sizeof(int)) bits of memory. The second algorithm, which never generates the random fields, scales in time as O(N \log N) and asymptotically needs storage of only one bit per spin, about 96 times less memory than the first algorithm. We present results for system sizes of up to a billion spins, which can be run on a workstation with 128MB of RAM in a few hours. We also show that important physical questions were resolved only with the largest of these simulations.

References in corpus (3)

• Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
• Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
• Depinning of a domain wall in the 2d random-field Ising model

Cited by in corpus (19)

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• Spanning avalanches in the three-dimensional Gaussian Random Field Ising Model with metastable dynamics: field dependence and geometrical properties
• Analysis of power-law exponents by maximum-likelihood maps
• Crackling Noise, Power Spectra and Disorder Induced Critical Scaling
• Random Field Ising Model In and Out of Equilibrium
• Origin of scale-free intermittency in structural first-order phase transitions
• Hysteresis and avalanches in the T=0 random-field Ising model with 2-spin-flip dynamics
• Determination of intrinsic switching field distributions in perpendicular recording media: numerical study of the $\Delta H(M,\Delta M)$ method
• Random Field Potts model with dipolar-like interactions: hysteresis, avalanches and microstructure
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Influence of the aspect ratio and boundary conditions on universal finite size scaling functions in the athermal metastable 2d Random Field Ising Model
• Hysteresis in the T=0 RFIM: beyond metastable dynamics
• History-Induced Critical Behavior in Disordered Systems
• The dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields
• Diluted 3d-Random Field Ising Model at zero temperature with metastable dynamics
• The effects of external noise on threshold induced correlations in ferromagnetic systems