Spatial structures and dynamics of kinetically constrained models for glasses

TL;DR

This paper analyzes kinetically constrained lattice models for glasses, revealing how constraints induce slow dynamics, phase transitions, and cooperative behavior, with implications for understanding glassy systems' microscopic mechanisms.

Contribution

It provides a detailed analysis of the dynamics and phase transitions in kinetically constrained models, highlighting the role of mobile elements and spatial structures in glassy behavior.

Findings

Dynamical transition to a partially frozen phase on Bethe lattices.

Rare mobile elements destroy the transition in finite dimensions.

Mobile element spacing diverges exponentially as vacancy density decreases.

Abstract

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density, $v$, the spacing, $\Xi$, between mobile elements diverges exponentially or faster in $1/v$. Within the mobile elements, the dynamics is intrinsically cooperative and the characteristic time scale diverges faster than any power of $1/v$ (although slower than $\Xi$). The tagged-particle diffusion coefficient vanishes roughly as $\Xi^{-d}$.