Hysteresis loop area of the Ising model

Abstract

The hysteresis of the Ising model in a spatially homogeneous AC field is studied using both mean-field calculations and two-dimensional Monte Carlo simulations. The frequency dispersion and the temperature dependence of the hysteresis loop area are studied in relation to the dynamic symmetry loss. The dynamic mechanisms may be different when the hysteresis loops are symmetric or asymmetric, and they can lead to a double-peak frequency dispersion and qualitatively different temperature dependence.PACS numbers: 75.60. Ej, 75.40.Gb, 75.10.Hk When a cooperative many-body system, such as a magnet, is placed in an oscillating external perturbation (such as a magnetic field), it may show also oscillating dynamic response. This response usually lags in time, creating a hysteresis loop with nonzero area. This phenomenon exists widely in, e.g., magnetic systems and ferroelectric systems [1], and has been arousing great interest for its important technical application and intriguing physics [2][3][4].The recent theoretical [5-13] and experimental [14] studies on the hysteresis (also see Ref.[4] and references therein) focus on two topics: the dynamic symmetry breaking, and the area of the hysteresis loop. The first phenomenon is due to the competing time scales in such nonequilibrium systems [4]: The hysteresis loop loses its symmetry when the time period of the oscillating external perturbation becomes much smaller than the typical relaxation time of the system. On the other hand, the interesting variance of the hysteresis loop area with such parameters as temperature and oscillation frequency can also be attributed to the time scale competition. For example, in the frequency dispersion of the loop area of the Ising model, the frequency ω 0 /2π giving the maximal area corresponds roughly to the point where a resonance occurs. When an Ising system is placed in an AC field, the dynamics may consist of domain nucleation and/or domain growth [3]. The nucleation rate of new domains can be predicted by a characteristic time τ n , and the domain growth rate is also linked with a characteristic time τ g . The resonance occurs when the time period of the external perturbation is comparable to either one of these time scales or a combination of them. As is shown below, the details of this dynamic time scale competition necessarily rely on the dynamic phase of the system.In the present work, we hope to help clarify the relationship of the two mentioned-above topics in the framework of the Ising model, with mean-field (MF) calculations and two-dimensional Monte-Carlo (MC) simulations. (The frequency range that receives the most attention here is within the discussion of the previous works using the same methods [4].) When the loops are symmetric, the system dynamics is controlled by a domain nucleation-and-growth mechanism. When the loops are asymmetric (especially when the magnetization is well above or below zero), throughout the system evolution we can observe most spins being in the same direction. The dynamics of the remainin...

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