Hysteresis, Avalanches, and Barkhausen Noise

TL;DR

This paper investigates the origin of power-law distributions in hysteresis and avalanches using the zero temperature random field Ising model, revealing critical points and extensive scaling behavior across multiple dimensions.

Contribution

It demonstrates the existence of a critical point with scale-invariant avalanches in the model and shows power-law scaling occurs over a broad range of disorder levels.

Findings

Critical point with avalanches on all scales identified.

Power-law distributions observed far from the critical point.

Extensive scaling behavior confirmed in multiple dimensions.

Abstract

Hysteresis, the lag between the force and the response, is often associated with noisy, jerky motion which have recently been called ``avalanches''. The interesting question is why the avalanches come in such a variety of sizes: naively one would expect either all small events or one large one. Power-law distributions are often seen near transitions, or critical points. We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. We study this critical point in 6-epsilon dimensions, and with simulations in 2, 3, 4, 5, 7, and 9 dimensions with systems as large as 1000^3. The power-law distributions in principle only occur for a special value of the randomness (the critical point), but many decades of scaling occur quite far from this special value: three decades of scaling (a publishable experiment) are obtained a factor of two away from the critical value. Perhaps many of the power laws observed in nature are just systems near their critical points?