2014/05/31 by Peter G. Fennell, James P. Gleeson, Davide Cellai
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Dynamics (music) #Glass transition #Liquid Crystal Research Advancements #Master equation #Material Dynamics and Properties #Mathematics #Monte Carlo method #Phase (matter) #Phase diagram #Phase transition #Physics #Polymer #Quantum mechanics #Relaxation (psychology) #Spin glass #Spins #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #math.DS
paper · pdf · doi:10.1103/physreve.90.032824
published as Phys. Rev. E 90, 032824 (2014) · 10 pages, 5 figures, 2 tables
openalex publication_date 2014/09/30 · arxiv created 2014/11/06 · arxiv updated 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic signatures of the structural relaxation properties of glass-forming liquids. While the equilibrium phase diagram of these models can be calculated analytically, the dynamics are usually investigated numerically. Here we propose a network-based approach, called approximate master equation (AME), to the dynamics of the Fredrickson-Andersen model. The approach correctly predicts the critical temperature at which the glass transition occurs. We also find excellent agreement between the theory and the numerical simulations for the transient regime, except in close proximity of the liquid-glass transition. Finally, we analytically characterize the critical clusters of the model and show that the departures between our AME approach and the Monte Carlo can be related to the large interface between blocked and unblocked spins at temperatures close to the glass transition.