Random hysteresis loops

Gioia Carinci

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 2, page 307-339
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Carinci, Gioia. "Random hysteresis loops." Annales de l'I.H.P. Probabilités et statistiques 49.2 (2013): 307-339. <http://eudml.org/doc/271981>.

@article{Carinci2013,
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 $N^\{-2/3\}$, $N$ the size of the system, the “critical” hysteresis loop becomes random.},
author = {Carinci, Gioia},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {hysteresis; Ising; mean field Glauber dynamics; macroscopic fluctuations; ferromagnetic Ising model; mean-field Glauber dynamics; Langevin-type equation; critical behavior; martingales; stopping times; tightness; limiting probability laws},
language = {eng},
number = {2},
pages = {307-339},
publisher = {Gauthier-Villars},
title = {Random hysteresis loops},
url = {http://eudml.org/doc/271981},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Carinci, Gioia
TI - Random hysteresis loops
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 2
SP - 307
EP - 339
AB - 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.
LA - eng
KW - hysteresis; Ising; mean field Glauber dynamics; macroscopic fluctuations; ferromagnetic Ising model; mean-field Glauber dynamics; Langevin-type equation; critical behavior; martingales; stopping times; tightness; limiting probability laws
UR - http://eudml.org/doc/271981
ER -

References

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