Bootstrap percolation and kinetically constrained models on hyperbolic lattices

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, $0<{\rho }_c<1$. 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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• Percolation on hyperbolic lattices
• Hard Discs on the Hyperbolic Plane
• Spiral Model: a cellular automaton with a discontinuous glass transition
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Cited by in corpus (9)

• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Critical behavior in spherical and hyperbolic spaces
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• Solvable Models of Supercooled Liquids in Three Dimensions
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Crossing on hyperbolic lattices
• Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
• Kinetically constrained spin models on trees
• Constraint percolation on hyperbolic lattices