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Bootstrap percolation and kinetically constrained models on hyperbolic lattices | | François Sausset
; Cristina Toninelli
; Giulio Biroli
; Gilles Tarjus
; | | Date: |
6 Jul 2009 | | Abstract: | We study bootstrap percolation (BP) on hyperbolic lattices obtained by
regular tilings of the hyperbolic plane. Our work is motivated by the
connection between the BP transition and the dynamical transition of
kinetically constrained models, which are in turn relevant for the study of
glass and jamming transitions. We show that for generic tilings there exists a
BP transition at a nontrivial critical density, $0<
ho_c<1$. Thus, despite the
presence of loops on all length scales in hyperbolic lattices, the behavior is
very different from that on Euclidean lattices where the critical density is
either zero or one. Furthermore, we show that the transition has a mixed
character since it is discontinuous but characterized by a diverging
correlation length as it occurs on Bethe lattices and random graphs of constant
connectivity. | | Source: | arXiv, 0907.0938 | | Services: | Forum | Review | PDF | Favorites | |
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