Kim Mina, Park Su-Chan, Noh Jae Dong
Department of Physics, University of Seoul, Seoul 130-743, Korea.
Department of Physics, The Catholic University of Korea, Bucheon 420-743, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):012132. doi: 10.1103/PhysRevE.91.012132. Epub 2015 Jan 16.
We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any u<1 exhibiting the power-law scaling of the characteristic length scale ξ∼t(1/z) and the domain-wall density ρ∼t(-δ). The scaling exponents z and δ were found to vary continuously with the parameter u. To establish the anomalous power-law scaling firmly, we perform the block renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.
我们对具有手性的一维非平衡伊辛自旋系统的有序动力学进行了数值研究。该系统的特征是自旋更新规则依赖于方向。+-自旋对可以以概率(1 - u)翻转到++或--，或以概率u翻转到-+，而-+对则保持不变。研究发现，在任何u < 1的情况下，系统都会演变成铁磁有序状态，呈现出特征长度尺度ξ∼t(1/z)和畴壁密度ρ∼t(-δ)的幂律标度。发现标度指数z和δ随参数u连续变化。为了牢固地确立反常幂律标度，我们进行了由巴苏和欣里希森[U. Basu和H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]提出的块重整化分析。块重整化方法在动态标度不变性的假设下预测了一个标度关系，可用于数值估计标度指数。我们找到了标度关系成立的条件。然后我们将该方法应用于我们的模型，并在几个u值下获得了临界指数zδ。数值结果与先前的研究结果完全一致。这项研究为非平衡手性伊辛模型表现出具有连续变化指数的幂律标度行为这一说法提供了额外的证据。
