Olga Perkovic

AVALANCHES, BARKHAUSEN NOISE, AND PLAIN OLD CRITICALITY

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{percent} above the critical point, where two decades of scaling are still observed. We simulate systems with up to 1000{sup 3} domains, extract critical exponents in 2, 3, 4, and 5 dimensions, compare with our 2D and 6{minus}{epsilon} predictions, and compare to a variety of experiments. {copyright} {ital 1995 The American Physical Society.}

Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions

We present numerical simulations of avalanches and critical phenomena associated with hysteresis loops, modeled using the zero-temperature random-field Ising model. We study the transition between smooth hysteresis loops and loops with a sharp jump in the magnetization, as the disorder in our model is decreased. In a large region near the critical point, we find scaling and critical phenomena, which are well described by the results of an {epsilon} expansion about six dimensions. We present the results of simulations in three, four, and five dimensions, with systems with up to a billion spins (1000{sup 3}). thinsp {copyright} {ital 1999} {ital The American Physical Society}

Random-field ising models of hysteresis

This chapter presents the results of the simulations and analysis. The arguments for the applicability of the model of hysteresis are based on renormalization group and scaling theories, first developed to study continuous-phase transitions in equilibrium systems. To a large extent, these theories can be seen as the underlying reason for many theories of nature being applied to the real world, and (more specifically) different magnets sharing common features in their dynamics despite having microscopically different morphologies and energetics. A successful theory should predict statistical averages of almost any quantity that is dominated by events on large length and time scales, up to certain overall parameter-dependent scales (analogous to viscosity and density for fluids).

Hysteresis, avalanches, and noise

In our studies of hysteresis and avalanches in the zero-temperature random-field Ising model, a simple model of magnetism, we often have had to do very large simulations. Previous simulations were usually limited to relatively small systems (up to 900/sup 2/ and 128/sup 3/), although there have been exceptions. In our simulations, we have found that larger systems (up to a billion spins) are crucial to extracting accurate values of the critical exponents and understanding important qualitative features of the physics. We show three algorithms for simulating these large systems. The first uses the brute-force method, which is the standard method for avalanche-propagation problems. This algorithm is simple but inefficient. We have developed two efficient and relatively straightforward algorithms that provide better results. The sorted-list algorithm decreases execution time, but requires considerable storage. The bits algorithm has an execution time that is similar to that of the sorted-list algorithm, but it requires far less storage.

Hysteresis, Avalanches, and Barkhausen Noise

We’ve been working on the crackling noise in hysteresis loops [1, 2, 3, 4, 5, 6]. Hysteresis occurs when you push and pull on a system with an external force, and the response lags behind the force. The hysteresis loop is the graph of force (say, an external magnetic field H) versus the response (say, the magnetization M of the material). In many materials, the hysteresis loop is not actually microscopically smooth: it is composed of small bursts, or avalanches (figure 1). In many first-order phase transitions, these bursts cause acoustic emission (crackling noise); in magnets, they are called Barkhausen noise.

Hysteresis and avalanches: phase transitions and critical phenomena in driven disordered systems

Abstract We discuss Barkhausen noise in magnetic systems in terms of avalanches near a disorder-induced critical point, using the hysteretic zero-temperature random-field Ising model and recent variants. As the disorder is decreased, one finds a transition from smooth hysteresis loops to loops with a sharp jump in magnetization (corresponding to an infinite avalanche). In a large region near the transition point the model exhibits power-law distributions of noise (avalanches), universal behavior and a diverging length scale. Universal properties of this critical point are reported that were obtained using renormalization group methods and numerical simulations. Connections to other experimental systems such as athermal martensitic phase transitions (with and without ‘bursts’) and front propagation are also discussed.

IMPROVED MAGNETIC INFORMATION STORAGE USING RETURN-POINT MEMORY

The traditional magnetic storage mechanisms (both analog and digital) apply an external field signal H(t) to a hysteretic magnetic material, and read the remanent magnetization M(t), which is (roughly) proportional to H(t). We propose a new analog method of recovering the signal from the magnetic material, making use of the shape of the hysteresis loop M(H). The field H, “stored’’ in a region with N domains or particles, can be recovered with fluctuations of order 1/N using the new method—much superior to the 1/N fluctuations in traditional analog storage.