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20 September 2020
  » arxiv » 0907.0938

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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
AbstractWe 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
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