Zero-temperature dynamics of the weakly disordered Ising model
Zero-temperature dynamics of the weakly disordered Ising model
复制标题
DOI：
10.1103/physreve.59.r2493
复制
发表时间：
1999-03
影响因子：
2.4
通讯作者：
S. Jain
中科院分区：
文献类型：
--
作者：
S. Jain
在零温度下研究了纯弱无序随机键二维伊辛模型的格劳伯动力学。从等时间相关函数中提取单个特征长度尺度 $L(t)$。在纯情况下，持续概率随着长度尺度的粗化而呈代数下降。在无序的情况下，确定了三种不同的状态：行为类似纯粹的短时间状态；持久概率随时间非代数衰减的中间状态；以及领域冻结和增长停止的长期制度。在中间状态下，我们发现 $P(t)\sim L(t)^{-\theta'}$，其中 $\theta' = 0.420\pm 0.009$。 $\theta'$ 的值与零温下纯二维伊辛模型的值一致。我们在中间状态下的结果与持续概率随时间的对数衰减一致，$P(t)\sim (\ln t)^{-\theta_d}$，其中$\theta_d = 0.63\pm 0.01$。
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.