临界粗化中的动力学不均匀性：有限尺寸球形模型中相关和响应起伏的精确结果
Dynamic heterogeneities in critical coarsening: Exact results for correlation and response fluctuations in finite-sized spherical models
摘要：
我们研究了球形铁磁体从无限温度到临界点失超后的非平衡粗化动力学中的动力学不均匀性。探测这种不均匀性的标准方法是通过监测相关性和磁化率的波动，粗粒度的介观区域。我们讨论了如何定义波动的粗粒度的相关性（C）和磁化率（Chi）的模型中，没有淬火无序。我们对球形模型的关注点是在整个$N$自旋体积上的粗粒化，这需要考虑自旋的N^{-1/2}个非高斯波动。后者被视为一个扰动的领先阶高斯统计。我们得到了这些量的精确结果，这使我们能够确定C和Chi涨落的联合分布。我们发现，这种分布是定性不同的，即使是临界以上的平衡，从自旋玻璃的情况下，C和志波动的方式类似于平均C和志之间的波动耗散关系。我们的研究结果表明，粗化在临界d>4明显是不均匀的，并建议，在其他玻璃体系中，有一个明确的时间尺度上的波动在整个热历史是最大的。然而，令人惊讶的是，这个时间尺度和非均匀性的幅度都没有随着系统的年龄而增加，正如从不断增长的相关长度所预期的那样。当d<4时，涨落的强度在与系统年龄成比例的时间尺度上变化;相应的振幅也随年龄增长，但并不像人们天真地预期的那样与相关体积成比例。
英文摘要：
We study dynamic heterogeneities in the out-of-equilibrium coarsening dynamics of the spherical ferromagnet after a quench from infinite temperature to its critical point. A standard way of probing such heterogeneities is by monitoring the fluctuations of correlation and susceptibility, coarse-grained over mesoscopic regions. We discuss how to define fluctuating coarse-grained correlations (C) and susceptibilities (Chi) in models where no quenched disorder is present. Our focus for the spherical model is on coarse-graining over the whole volume of $N$ spins, which requires accounting for N^{-1/2} non-Gaussian fluctuations of the spin. The latter are treated as a perturbation about the leading order Gaussian statistics. We obtain exact results for these quantities, which enable us to characterise the joint distribution of C and Chi fluctuations. We find that this distribution is qualitatively different, even for equilibrium above criticality, from the spin-glass scenario where C and Chi fluctuations are linked in a manner akin to the fluctuation-dissipation relation between the average C and Chi. Our results show that coarsening at criticality is clearly heterogeneous for d>4 and suggest that, as in other glassy systems, there is a well-defined timescale on which fluctuations across thermal histories are largest. Surprisingly, however, neither this timescale nor the amplitude of the heterogeneities increase with the age of the system, as would be expected from the growing correlation length. For d<4, the strength of the fluctuations varies on a timescale proportional to the age of the system; the corresponding amplitude also grows with age, but does not scale with the correlation volume as might have been expected naively.
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