Random Hysteresis Loops

TL;DR

This paper investigates the behavior of hysteresis loops in the mean-field Ising model under Glauber dynamics, showing that at specific oscillation frequencies, the hysteresis loop becomes inherently random.

Contribution

It provides a rigorous analysis of the emergence of randomness in hysteresis loops at critical frequencies in the mean-field Ising model.

Findings

Hysteresis loops become random at frequencies of order N^{2/3}.

The study connects oscillation frequency with the stochastic nature of hysteresis.

Results are derived for the mean-field Ising model with Glauber dynamics.

Abstract

Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order $N^{2/3}$, with $N$ the size of the system, the "critical" hysteresis loop becomes random.