Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model

TL;DR

This paper demonstrates that the Sherrington-Kirkpatrick model exhibits self-organized criticality throughout the hysteresis loop, capturing key physics of disordered ferromagnetic systems with long-range interactions.

Contribution

It introduces the application of the SK model to hysteresis phenomena in random ferromagnets, showing self-organized criticality via scaling, replica, and numerical methods.

Findings

System exhibits self-organized criticality across the entire hysteresis loop.

Distribution functions of avalanches, jumps, and local fields are characterized.

The model captures essential physics of systems with frustration and long-range interactions.

Abstract

We study hysteretic phenomena in random ferromagnets. We argue that the angle dependent magnetostatic (dipolar) terms introduce frustration and long range interactions in these systems. This makes it plausible that the Sherrington - Kirkpatrick model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations and large scale numerical simulations to characterize the hysteresis of the zero temperature SK model. By constructing the distribution functions of the avalanche sizes, magnetization jumps and local fields, we conclude that the system exhibits self-organized criticality everywhere on the hysteresis loop.