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

Mauro Sellitto·Giulio Biroli·Cristina Toninelli
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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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Mauro Sellitto, Giulio Biroli, Cristina Toninelli. 2004-12-06. Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics. https://doi.org/10.1209/epl%2Fi2004-10372-5

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