Hysteresis, Avalanches, and Noise: Numerical Methods

TL;DR

This paper introduces two efficient algorithms for simulating large-scale hysteresis and noise phenomena in the random-field Ising model, enabling analysis of systems with up to a billion spins.

Contribution

Development of two scalable algorithms for large-system simulations of hysteresis and avalanches in the random-field Ising model at zero temperature.

Findings

Algorithms enable simulations of up to a billion spins.

Largest simulations resolved key physical questions.

Memory-efficient algorithm uses only one bit per spin.

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.