Zero-temperature Avalanche Criticality Governing Dynamical Heterogeneity in Supercooled Liquids

Abstract

In supercooled liquids, mesoscale mobile and immobile domains are ubiquitously observed, a phenomenon known as dynamical heterogeneity. Extensive studies have established that the characteristic size of these domains grows upon cooling and exhibits system-size dependence. However, the physical origin of this domain growth remains a matter of active debate. In this work, using molecular simulations, we demonstrate that the temperature and system-size dependence of dynamical heterogeneity can be explained within a zero-temperature avalanche criticality picture.

Figures (5)

• Figure 1: (a–d) Snapshots illustrating the growth of dynamical domains. Each panel shows the displacement magnitude field relative to a reference configuration at the times indicated in panels (e) and (f). Only particles with displacement magnitudes exceeding $a = 0.3$ are shown. Warmer (cooler) colors represent larger (smaller) displacements. (e) Semi-log plot showing the time evolution of the averaged overlap function $Q(t)$. (f) Semi-log plot showing the time evolution of the dynamical susceptibility $\chi_4(t)$. All panels show results for $N = 1000$ and $T = 0.44$.
• Figure 2: Log-log plots of the peak value of the dynamical susceptibility, $\chi_4^\ast$, as a function of $T$ in the scaling regime $T \le T_{\rm ava} \approx 0.6$. (a) Raw data. (b) Finite-size scaling collapse. Symbols denote different system sizes, as indicated in the legend. The dashed line shows the power-law scaling $\chi_4^\ast \sim T^{-\gamma}$.
• Figure 3: (a) Log-log plots of the two correlation lengths, $\xi$ and $\xi_\chi$ (the latter extracted from $\chi_4^\ast$ at $N=1000$), as functions of temperature $T$. The dashed line indicates the power-law fit to $\xi$ in the scaling regime. (b) Log-log plots of the temperature dependence of the fraction of unstable modes at saddle-point configurations, $f_{\rm saddle}^\dagger$. Symbols denote different system sizes, as indicated in the legend. The dashed line indicates the power-law fit in the scaling regime for $N = 1000$. In both panels, the shaded region marks the scaling regime $T \le T_{\rm ava}$.
• Figure 4: (a) Log--log plot of the low-frequency part of the vibrational density of states of stable samples, $D^{\rm S}_0(\omega)$, as a function of the eigenfrequency $\omega$. Symbols distinguish different temperatures, as indicated in the legend. All results are for $N=1000$. The dotted lines represent fits to $A_{\rm S}\omega^{6.5}$. (b) Log--log plot of $A_{\rm S}$ as a function of temperature. The same symbols are used for the three temperatures shown in panel (a).
• Figure 5: (a) Log--log plot of the displacement-based dynamical susceptibility $\tilde{\chi}_4^\ast$ as a function of temperature. Results after finite-size scaling are shown. Symbols have the same meaning as in Fig. \ref{['fig:chi_4']}. The dashed line represents $T^{\tilde{\gamma}}$. (b) Log--log plot of $D\tau_x$ as a function of temperature, shown for $N=1500$. Symbols distinguish different time scales, as indicated in the legend. The dashed line represents the prediction of Eq. \ref{['eq:SEvio']}.