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