论文标题
在具有被捕状态的模型中，尺寸拉伸的指数放松
Size-Stretched Exponential Relaxation in a Model with Arrested States
论文作者
论文摘要
我们研究了与竞争相互作用的模型中快速淬灭至零温度的效果，从而通过保守的自旋动态发展。在模型参数的一定态度中，我们发现该模型属于更广泛的动力学约束模型，但是，动力学与玻璃的动力学不同。该系统显示出拉伸的指数放松，其不寻常的特征是放松时间作为系统尺寸的力量而发散。明确地，我们发现空间相关函数以$ \ exp（-2r/\ sqrt {l}）$延伸为具有稳定状态$ l $站点的空间分离$ r $的函数，而时间稳定状态的函数，而时间自动相关功能，而$ \ exp（ - 与$ l $成比例。在变形方案中，$ t_w $之后，有两个增长的长度尺度，即$ \ Mathcal {l}（t_w）（t_w）\ sim t_w^{1/2} $和$ \ Mathcal {r}（r}（t_w）（t_w）\ sim t_w^^{1/4} $;空间相关函数以$ \ exp（-r/ \ mathcal {r}（t_w））$衰减。有趣的是，单个典型样本在稳态下的自动相关函数的拉伸指数形式与在不同淬火导致的初始条件的集合中平均不同。后者在很大程度上显示出缓慢的力量法律。
We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $\exp(-2r/\sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $\exp(-(t/τ_L)^{1/2})$, where $t$ is the time and $τ_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $\mathcal{L}(t_w) \sim t_w^{1/2}$ and $\mathcal{R}(t_w) \sim t_w^{1/4}$; the spatial correlation function decays as $\exp(-r/ \mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.
