Europhys. Lett.
Volume 69, Number 4, February 2005
Page(s) 496 - 502
Section General
Published online 14 January 2005
Europhys. Lett., 69 (4), pp. 496-502 (2005)
DOI: 10.1209/epl/i2004-10372-5

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

M. Sellitto1, G. Biroli2 and C. Toninelli3

1  The Abdus Salam International Centre for Theoretical Physics Strada Costiera 11, 34100 Trieste, Italy
2  Service de Physique Théorique, CEA/Saclay Orme des Merisiers, F-91191 Gif-sur-Yvette Cedex, France
3  Laboratoire de Physique Théorique, École Normale Supérieure 24 rue Lhomond, Paris, France

received 17 September 2004; accepted in final form 2 December 2004
published online 14 January 2005

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.

05.20.-y - Classical statistical mechanics.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
64.70.Pf - Glass transitions.

© EDP Sciences 2005