arXiv 2009.026352020-09-06cond-mat.softcond-mat.stat-mech

剪切玻璃中雪崩临界性的统一观点

Unified View of Avalanche Criticality in Sheared Glasses

Norihiro Oyama, Hideyuki Mizuno, Atsushi Ikeda

备注：: 16 pages, 16 figures
发表信息：: Phys. Rev. E 104, 015002 (2021)
DOI：: 10.1103/PhysRevE.104.015002

摘要：

剪切玻璃中的塑性事件被认为是所谓雪崩的一个例子，其大小服从幂律概率分布，雪崩临界指数为$τ$。虽然平均场论预测了该指数的普适值$τ_{\rm MF}=1.5$，但数值模拟报告了取决于文献的不同值。此外，在弹性状态下，人们注意到临界指数可能与稳态下的不同，甚至临界性本身也是一个有争议的问题。由于这些令人困惑的不同结果是在不同的设置下报告的，我们对剪切玻璃中雪崩临界性的了解非常有限。为了获得统一的理解，在这项工作中，我们进行了全面的数值研究雪崩在Lennard-Jones玻璃下的非热准静态剪切。特别是，通过排除模糊性和任意性，已经潜入到传统的测量方案，我们实现了高精度的测量，并证明了在稳态下的指数$τ$遵循平均场预测的$τ_{\rm MF}=1.5$。我们的研究结果还表明，有两个定性不同的雪崩事件。这种二进制导致雪崩尺寸分布的非普遍行为，并且可能是迄今为止报道的$τ$的变化值的原因。为了研究临界性和普适性对外加剪切的依赖性，我们进一步研究了弹性区域中雪崩的统计和不同样品中第一个雪崩事件的系综，这提供了未微扰系统的信息。我们表明，虽然未受扰的系统确实处于非临界状态，但随着剪切的施加，临界性逐渐发展。此外，临界指数服从平均场预测$τ_{\rm MF}$普遍，一旦系统成为临界。

英文摘要：

Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent $τ$. Although mean-field theory predicts a universal value of this exponent, $τ_{\rm MF}=1.5$, numerical simulations have reported different values depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results were reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent $τ$ in the steady state follows the mean-field prediction of $τ_{\rm MF}=1.5$. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the non-universal behavior of the avalanche size distribution and is likely to be the cause of the varying values of $τ$ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. Moreover, the critical exponent obeys the mean-field prediction $τ_{\rm MF}$ universally, once the system becomes critical.

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