Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics

TL;DR

This paper demonstrates that facilitated spin models on Bethe lattices exhibit glassy dynamics, including two-step relaxation and aging, akin to mode-coupling theory predictions and mean-field disordered systems, with a phase transition described by bootstrap percolation.

Contribution

It establishes a connection between facilitated spin models, bootstrap percolation, and glassy dynamics on Bethe lattices, highlighting their mean-field-like behavior.

Findings

Relaxation time diverges at a finite temperature following a power-law.

Displays two-step relaxation and aging phenomena.

Dynamical arrest corresponds to bootstrap percolation transition.

Abstract

We show that facilitated spin models of cooperative dynamics introduced by Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar to the one predicted by the mode-coupling theory of supercooled liquids and the dynamical theory of mean-field disordered systems. At low temperature such cooperative models show a two-step relaxation and their equilibration time diverges at a finite temperature according to a power-law. The geometric nature of the dynamical arrest corresponds to a bootstrap percolation process which leads to a phase space organization similar to the one of mean-field disordered systems. The relaxation dynamics after a subcritical quench exhibits aging and converges asymptotically to the threshold states that appear at the bootstrap percolation transition.