Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands.
Phys Rev E. 2019 Jul;100(1-1):012132. doi: 10.1103/PhysRevE.100.012132.
We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics. We obtain the dynamical scaling properties for these modes and use them to calculate the time evolution of two dynamical quantities for the system, namely, the autocorrelation function and the mean-square deviation of the line magnetizations. At intermediate times 1≲t≲L^{z_{c}}, where z_{c}=4-η=15/4 is the dynamical critical exponent of the model, we find that the line magnetization undergoes anomalous diffusion. Following our recent work on anomalous diffusion in spin models, we demonstrate that the generalized Langevin equation with a memory kernel consistently describes the anomalous diffusion, verifying the corresponding fluctuation-dissipation theorem with the calculation of the force autocorrelation function.
我们证明了在临界温度下，具有局域自旋交换运动（即 Kawasaki 动力学）的二维伊辛模型中，磁化强度的傅里叶模式是动力学本征模式。我们得到了这些模式的动力学标度性质，并利用它们来计算系统的两个动力学量的时间演化，即自相关函数和线磁化强度的均方偏差。在中间时间 1≲t≲L^{z_{c}} 中，其中 z_{c}=4-η=15/4 是模型的动力学临界指数，我们发现线磁化强度经历了反常扩散。根据我们最近在自旋模型中的反常扩散研究，我们证明了具有记忆核的广义朗之万方程一致地描述了反常扩散，通过计算力自相关函数验证了相应的涨落耗散定理。
