On the study of jamming percolation

Abstract

We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.

13 pages, 18 figures; Spiral model does satisfy property B

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• Network Analysis of Particles and Grains
• On the study of force-balance percolation
• Correlated percolation and tricriticality
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Jamming Mechanisms and Density Dependence in a Kinetically-Constrained Model
• Jamming Percolation in Three Dimensions
• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications
• Contact processes in crowded environments
• Subcritical $\mathcal{U}$-bootstrap percolation models have non-trivial phase transitions
• Constraint relaxation leads to jamming