Collective Relaxation Dynamics in a Three-Dimensional Lattice Glass Model

We numerically elucidate the microscopic mechanisms controlling the relaxation dynamics of a three-dimensional lattice glass model that has static properties compatible with the approach to a random first-order transition. At low temperatures, the relaxation is triggered by a small population of particles with low-energy barriers forming mobile clusters. These emerging quasiparticles act as facilitating defects responsible for the spatially heterogeneous dynamics of the system, whose characteristic length scales remain strongly coupled to thermodynamic fluctuations. We compare our findings both with existing theoretical models and atomistic simulations of glass formers.

Figure 1

(a),(b) Temperature evolution of the collective overlap $⟨Q(t)⟩$. (c) Arrhenius plot of the relaxation time ${\tau }_{\alpha }$; the broken line is an Arrhenius fit valid at high temperatures. (d) Relaxation spectrum from Eq. (3); dashed curves represent the spectrum corresponding to the final stretched exponential decay of the overlap.

Figure 2

(a) Time dependence of the MSD; diffusive behavior is indicated with dashed lines. The van Hove distribution functions at (b) $T=0.4$ where ${\tau }_{\alpha }\simeq 2\times {10}^5$ and (c) $T=0.26$ where ${\tau }_{\alpha }\gg {10}^{10}$.

Figure 3

(a) Cumulative distribution of local energy barriers. The vertical line indicates $\mathrm{\Delta }e=0$. (b)–(d) Snapshots showing lattice sites with $\mathrm{\Delta }e\le 0$ at $T=0.3$ at three different times. The time intervals between (b) and (c) and between (c) and (d) are 50 and 350, respectively. Sites highlighted in red belong to a quasiparticle moving rapidly. (e) Lattice sites with states that differ between times 0 and $7\times {10}^4$, showing the superposition of multiple quasiparticle paths.

Figure 4

(a) Four-point correlation function $G_4(r,t)$ at $T=0.325$ where ${\tau }_{\alpha }\approx {10}^8$. (b) Dynamical susceptibility ${\chi }_4(t)$ and (c) dynamical length scale ${\xi }_4(t)$ demonstrating increasing dynamic heterogeneity.

Figure 5

Evolution of two estimates of a dynamic length scale, $({\chi }_4{)}^{1/3}$ and ${\xi }_4$, and of two estimates of a static correlation length scale $1/s(T)$ and $1/{ϵ}_c(T)$. Each quantity is normalized by its value at $T=0.45$. Inset shows $T\log ({\tau }_{\alpha })$ as a function of ${\xi }_4$; the dashed line is a fit to $\log ({\tau }_{\alpha })\sim {\xi }_4^{\psi }/T$ with $\psi =0.84$.