Unified View of Avalanche Criticality in Sheared Glasses

TL;DR

This study provides a comprehensive numerical analysis of avalanche criticality in sheared glasses, confirming the mean-field critical exponent in the steady state and revealing two types of avalanche events that explain previous discrepancies.

Contribution

It offers a high-precision measurement of the avalanche exponent and clarifies the conditions under which the mean-field prediction applies, unifying previous conflicting results.

Findings

Steady state avalanche exponent matches mean-field prediction of 1.5.

Identifies two qualitatively different avalanche events affecting distribution.

Criticality develops gradually with applied shear, with the exponent becoming universal once critical.

Abstract

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 $\tau$. Although mean-field theory predicts a universal value of this exponent, $\tau_{\rm MF}=1.5$, 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 $\tau$ in the steady state follows the mean-field prediction of $\tau_{\rm MF}=1.5$. 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 $\tau$ 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 $\tau_{\rm MF}$ universally, once the system becomes critical.