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

Preprint

6 December 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/0409393

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.

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All Related Versions

Version 1, 2004-09-15, ArXiv
Version 2, 2004-10-01, ArXiv
Version 3, 2004-12-06, ArXiv
Published version: Europhysics Letters, 69 (4), 496.

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