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25 January 2021
  » arxiv » cond-mat/0409393

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Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics
Mauro Sellitto ; Giulio Biroli ; Cristina Toninelli ;
Date 15 Sep 2004
Journal Europhys. Lett. 69 (4), 496 (2005)
Subject Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn
AbstractWe 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.
Source arXiv, cond-mat/0409393
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