Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.
Phys Rev E. 2018 May;97(5-1):052122. doi: 10.1103/PhysRevE.97.052122.
We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys. A 26, 2317 (1993)JPHAC50305-447010.1088/0305-4470/26/10/006]. The behavior of S(x,t), the probability that the walker is at position x at time t, is studied in detail. In general S(x,t)∼t^{-α}f(x/t^{α}) with α≃1 or 0.5 at large times depending on the parameters. In particular, S(x,t) for the point y=1,z=0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L^{2}logL. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S(x,t) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.
我们研究了经典自旋的动力学，将其映射为虚拟“自旋”空间中的步行者，使用由参数 y 和 z 特征化的广义双参数自旋模型族[de Oliveira 等人，J. Phys. A 26, 2317（1993）JPHAC50305-447010.1088/0305-4470/26/10/006]。详细研究了步行者在位置 x 处的概率 S(x,t)随时间 t 的行为。一般来说，S(x,t)∼t^{-α}f(x/t^{α})，其中 α≃1 或 0.5 在大时间取决于参数。特别是，对于对应于 Voter 模型的 y=1,z=0.5 点，S(x,t)显示出时间上的交叉；与这种交叉相关，可以定义两个时间尺度，它们随系统尺寸 L 变化为 L^{2}logL。我们还表明，当从无序区域沿着不同方向接近 Voter 模型点时，S(x,t)的高斯分布宽度以不同的指数方式呈幂律发散。对于大多数 Voter 情况，结果表明虚拟行走可能比其他非平衡方法更有效地检测相变。
