Abstract

Kinetic Ising ferromagnet, a bistable system, is studied in two dimensions on large systems under a time-varying sinusoidal external magnetic field of a fixed period P and different amplitudes \(h_0\). Far below the critical temperature \(T_c\) of ferro to paramagnet transition of the equilibrium zero-field Ising model, another critical temperature \(\theta _c\) is found to exist below which the system is in dynamic ordered phase (DOP) and above which the system is in dynamic disordered phase (DDP). Two important aspects of a bistable system under external time varying field, hysteresis and dynamic phase transition (DPT) are studied performing extensive numerical simulations. The hysteresis loops are asymmetric in DOP whereas they are symmetric in DDP. The hysteresis loop properties are estimated, developing a new methodology which provides information on loop orientation \(\alpha \) and its aspect ratio \(\varPhi \) over the usual properties such as area A and dynamic correlation C. The DPT occurs at a temperature \(\theta _c\) (\(\ll T_c\)) at which the mean metastable lifetime \(\langle \tau \rangle \) becomes comparable to the half period \(P_{1/2}\) of the applied filed. Though the smaller systems at higher field amplitudes are found to be in the stochastic resonance regime, the larger systems at all field amplitudes are found to display a continuous transition. The DPT is characterized by the critical exponents of 2d equilibrium Ising model. Discontinuous transition due to stochastic resonance at high field regime seems to be a finite size effect for the DPT under a sinusoidal oscillating field.

Graphic abstract

中文翻译：

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正弦振荡外部磁场下的动力学Ising模型：磁滞和动态相变

摘要

在固定时间周期P和不同振幅\（h_0 \）的时变正弦外部磁场下，在大型系统上二维地研究了双稳态系统Ising铁磁体。远低于平衡零场Ising模型的铁磁转变为顺磁体的临界温度\（T_c \），另一个临界温度\（\ theta _c \）发现存在于该系统之下，该系统处于动态有序阶段（DOP），在该系统之上，该系统处于动态无序阶段（DDP）。对双稳态系统在外部时变场下的两个重要方面，磁滞和动态相变（DPT）进行了研究，并进行了广泛的数值模拟。磁滞回线在DOP中是不对称的，而在DDP中是对称的。估计磁滞回线的特性，从而开发出一种新的方法，该方法可提供有关回线方向\（\ alpha \）及其宽高比\（\ varPhi \）的信息，这些信息通常位于面积A和动态相关C等常规属性上。DPT发生在温度\（\ theta _c \）（\（\ ll T_c \））的平均亚稳态寿命\（\ langle \ tau \ rangle \）变得与所申请字段的半周期\（P_ {1/2} \）相当。尽管发现较高场振幅的较小系统处于随机共振状态，但发现所有场振幅的较大系统均显示出连续的跃迁。DPT的特征在于二维平衡伊辛模型的临界指数。在正弦振荡场下，高场条件下由于随机共振而产生的不连续跃迁似乎是DPT的有限尺寸效应。

图形摘要