Random hysteresis loops

Carinci, Gioia

Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 2, pp. 307-339.

L’hystérésis dynamique est un phénomène qu’on observe dans les systèmes ferromagnétiques au-dessous de la temperature critique, en réponse à des variations adiabatiques du champ magnétique extérieur. Nous étudions le problème dans le contexte du modéle d’Ising de champ moyen avec la dynamique de Glauber, en montrant que, pour des fréquences d’oscillations du champ magnétique d’ordre de $N^{-2/3}$, avec $N$ la taille du système, la boucle d’hystérésis « critique » devient aléatoire.

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 $N^{-2/3}$, $N$ the size of the system, the “critical” hysteresis loop becomes random.

Classification : 82C20
Mots clés : hysteresis, Ising, mean field Glauber dynamics, macroscopic fluctuations

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