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Emergent facilitation by random constraints in a facilitated random walk model of glass

Leo S. I. Lam1, Hai-Yao Deng2, Wei-Bing Zhang3, Udoka Nwankwo1, Chu Xiao4, Cho-Tung Yip4, Chun-Shing Lee4,*, Haihui Ruan1,†, and Chi-Hang Lam5,‡

  • *Contact author: anakin-cs@hotmail.com
  • †Contact author: haihui.ruan@polyu.edu.hk
  • ‡Contact author: C.H.Lam@polyu.edu.hk
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Phys. Rev. E 111, 044120 – Published 14 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044120

Abstract

The physics of glass has been a significant topic of interest for decades. Dynamical facilitation is widely believed to be an important characteristic of glassy dynamics, but the precise mechanism is still under debate. We propose a lattice model of glass called the facilitated random walk (FRW). Each particle performs a continuous time random walk in the presence of its own random local kinetic constraints. The particles do not interact energetically. Instead, they interact kinetically with a hopping rate resampling rule under which motions of a particle can randomly perturb the local kinetic constraints of other particles. This dynamic interaction is reversible, following a rate restoration rule. A step-by-step reversal of the particle motions exactly restores the previous constraints, modeling randomness quenched in the configuration space of glass. The model exhibits stretched exponential relaxation and dynamical heterogeneity typical of glasses. Despite the lack of an explicit facilitation rule, the FRW shows facilitation behaviors closely analogous to those of the kinetically constrained models (KCM). The FRW is a coarse-grained version of the distinguishable particle lattice model (DPLM) and this exemplifies that compatible defect and atomistic models can complement each other in the study of glass.

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Phys. Rev. E 111, 044120– Published 14 April, 2025
  • Received 13 December 2024
  • Accepted 12 March 2025
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