Analytical approach to the dynamics of facilitated spin models on random networks

TL;DR

This paper introduces an approximate master equation (AME) approach to analytically study the dynamics of facilitated spin models on random networks, accurately predicting the glass transition and characterizing critical clusters.

Contribution

The paper presents a novel network-based AME method for analyzing facilitated spin model dynamics, improving understanding of glass transition phenomena.

Findings

AME accurately predicts the critical temperature for the glass transition.

Excellent agreement between theory and simulations away from the transition.

Analytical characterization of critical clusters and interface effects near the transition.

Abstract

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 new 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 frozen and unfrozen spins at temperatures close to the glass transition.