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 randomfield 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.
 Publication:

arXiv eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.condmat/9809122
 arXiv:
 arXiv:condmat/9809122
 Bibcode:
 1998cond.mat..9122K
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Materials Science;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Computing in Science and Engineering 1, 73 (1999)