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Facilitated spin models on Bethe lattice : bootstrap percolation , mode-coupling transition and glassy dynamics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sellitto, Mauro Biroli, Giulio Toninelli, Cristina |
| Copyright Year | 2008 |
| 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 powerlaw. 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. Introduction. – Lattice models are widely used in statistical mechanics to gain a qualitative and often deeper understanding of physical phenomena. In a seminal work Fredrickson and Andersen (FA) [1] introduced a simple lattice spin model of the liquid-glass transition, whose Hamiltonian corresponds to uncoupled Ising spins in a positive magnetic field [2, 3]. The spins represent a coarse-grained region of the liquid with high (−1 spins) or low (+1 spins) mobility and the magnetic field, that favors up spins, leads to very few mobile regions embedded in an immobile background at low temperature. The spin dynamics is subjected to a kinetic constraint: for each time step a randomly selected spin can flip only if the number of nearest neighbor down spins is larger or equal than f , where the facilitation parameter f is a number between zero and the lattice connectivity. The kinetic constraint mimics at a coarse grained level the cage effect in super-cooled liquids, where particles rattle in the cage formed by their neighbors and then move further if they are able to find a way through the surrounding particles. At low temperature/high density the latter process is strongly inhibited leading to an arrest of particle motion over macroscopic time scales. Similarly, at high temperature the kinetic constraint plays a little role and the relaxation is fast, whereas at low temperature |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/0409393v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/0409393v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/cond-mat/0409393v3.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Bethe lattice Bethe–Salpeter equation Booting Bootstrap percolation Bootstrapping (statistics) Cold Temperature Embedded system Embedding Exhibits as Topic Fever Ising model Kinetics Large Lattice model (physics) Like button Linear programming relaxation Liquid substance Magnetic Fields Mode coupling Physical Phenomena Population Parameter Randomness Rattle GUI Single Linkage Cluster Analysis Spin model Statistical Mechanics facilitation |
| Content Type | Text |
| Resource Type | Article |
