Refined universality for critical KCM: upper bounds

Abstract

We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions. They are tightly linked to the monotone cellular automata called bootstrap percolation. Among the three classes of such models, the critical ones are the most studied. Together with the companion paper by Marêché and the author, our work determines the logarithm of the infection time up to a constant factor for all critical KCM. This was previously known only up to logarithmic corrections. We establish that on this level of precision critical KCM have to be classified into seven categories. This refines the two classes present in bootstrap percolation and the two in previous rougher results. In the present work we establish the upper bounds for the novel five categories and thus complete the universality program for equilibrium critical KCM. Our main innovations are the identification of the dominant relaxation mechanisms and a more sophisticated and robust version of techniques recently developed for the study of the Fredrickson-Andersen 2-spin facilitated model.

arXiv comment100 pages, including 3 online-only appendices, 10 figures; comprehensive summary of mechanisms in section 2; changes: none (updated creative commons license)

References in corpus (11)

• Glassy dynamics of kinetically constrained models
• The Asymmetric One-Dimensional Constrained Ising Model
• Monotone cellular automata in a random environment
• Universality results for kinetically constrained spin models in two dimensions
• The second term for two-neighbour bootstrap percolation in two dimensions
• Refined universality for critical KCM: lower bounds
• Sharp threshold for the FA-2f kinetically constrained model
• Coalescing and branching simple symmetric exclusion process
• Combinatorics for general kinetically constrained spin models
• Bisection for kinetically constrained models revisited
• Fixation for Two-Dimensional $\mathcal{U}$-ISING and $\mathcal{U}$-VOTER Dynamics

Cited by in corpus (3)

• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications
• Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
• Locality approach to the bootstrap percolation paradox