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Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices

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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<ρ 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, similarly to what happens on Bethe lattices and random graphs of constant connectivity.

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Authors and Affiliations

  1. Institut de Physique de Théorique, CEA, CNRS, URA 2306, 91191, Gif sur Yvette, France

    François Sausset & Giulio Biroli

  2. Laboratoire de Probabilités et Modèles Aléatoires, CNRS UMR 7599, Université Pierre et Marie Curie et Université Denis Diderot, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Cristina Toninelli

  3. Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, UMR CNRS 7600, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Gilles Tarjus

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  1. François Sausset
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  2. Cristina Toninelli
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  3. Giulio Biroli
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  4. Gilles Tarjus
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Correspondence to François Sausset.

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Sausset, F., Toninelli, C., Biroli, G. et al. Bootstrap Percolation and Kinetically Constrained Models on Hyperbolic Lattices. J Stat Phys 138, 411–430 (2010). https://doi.org/10.1007/s10955-009-9903-1

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