Clarification of the Bootstrap Percolation Paradox

Abstract

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory, and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.

4 pages with 3 figures

References in corpus (4)

• Hysteresis in the Random Field Ising Model and Bootstrap Percolation
• Abelian Cascade Dynamics in Bootstrap Percolation
• Bistability and hysteresis in tilted sandpiles
• Threshold value of three dimensional bootstrap percolation

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• Renormalization group study of a kinetically constrained model for strong glasses
• Do current-density nonlinearities cut off the glass transition?
• Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem
• Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics
• Finite-size effects for anisotropic bootstrap percolation: logarithmic corrections
• Geometry of Empty Space is the Key to Near-Arrest Dynamics
• Finite Energy Extension of a Lattice Glass Model
• On $k$-Core Percolation in Four Dimensions
• Jamming percolation and glassy dynamics
• Dynamics of k-core percolation
• K-core attack, equilibrium K-core, and kinetically constrained spin system
• Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks
• Fredrickson--Andersen model in two dimensions
• Locality approach to the bootstrap percolation paradox