Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics
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.
Cite
@article{arxiv.cond-mat/0409393,
title = {Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics},
author = {Mauro Sellitto and Giulio Biroli and Cristina Toninelli},
journal= {arXiv preprint arXiv:cond-mat/0409393},
year = {2009}
}
Comments
7 pages, 6 figures, minor changes, final version to appear in Europhys. Lett