Abstract
One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.
Highlights
Glasses are amorphous materials whose rigidity emerges from the mutual caging of their constituent particles—be they atoms, molecules, colloids, grains, or cells
We consider the infinite-range variant of the hard sphere(s) (HS)based model proposed by Mari and Kurchan (MK) for simple structural glass formers [43,44,45]
The results illuminate the key role played by hopping in suppressing the ideal” random first-order transition (iRFOT) dynamical transition in finite d and in breaking the Stokes–Einstein relation (SER) scaling
Summary
We consider the infinite-range variant of the hard sphere(s) (HS)based model proposed by Mari and Kurchan (MK) for simple structural glass formers [43,44,45] (details in SI Text, section I.A). For a nontrivial distribution of cage sizes, thresholding volume exclusion maps cavity reconstruction onto void percolation for polydisperse spheres [50] (SI Text, section II.C). When φ > φp, they become finite and the mean network volume V net (sum of cage volumes in the network) follows a critical scaling from standard percolation (Fig. 4B) Based on this analysis, in the absence of facilitation the dynamical arrest should take place at φp [53]. Because the pressure at the dynamical transition increases only slowly with facilitation is notably signaled by the fact that the distribution of hopping times computed from a regular MD simulation largely coincides with the distribution obtained in the cavity procedure, where a single particle hops in an environment where neighboring particles are forbidden to do so (Fig. 3B, Inset). The limited number of ways out of a local cage entropically suppresses hopping
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