2009/07/31 by François Sausset, Cristina Toninelli, Giulio Biroli +1 · 19 citations
Materials Science · Mathematics · Physics and Astronomy · #Bethe lattice #Connection (principal bundle) #Constant (computer programming) #Euclidean geometry #Jamming #Percolation (cognitive psychology) #Quasicrystal Structures and Properties #Stable manifold #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Work (physics) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1007/s10955-009-9903-1
published in Journal of Statistical Physics 138(1-3), 411-430 (Springer Science+Business Media)
arxiv created 2009/12/10 · openalex publication_date 2009/12/11 · arxiv updated 2010/01/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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<ρc<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.