Refined universality for critical KCM: lower bounds

Abstract

We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions tightly linked to the monotone cellular automata called bootstrap percolation. There are three classes of such models, the most studied being the critical one. In a recent series of works it was shown that the KCM counterparts of critical bootstrap percolation models with the same properties split into two classes with different behaviour. Together with the companion paper by the first author, our work determines the logarithm of the infection time up to a constant factor for all critical KCM, which were previously known only up to logarithmic corrections. This improves all previous results except for the Duarte-KCM, for which we give a new proof of the best result known. We establish that on this level of precision critical KCM have to be classified into seven categories instead of the two in bootstrap percolation. In the present work we establish lower bounds for critical KCM in a unified way, also recovering the universality result of Toninelli and the authors and the Duarte model result of Martinelli, Toninelli and the second author.

arXiv comment56 pages, 3 figures; minor changes

References in corpus (13)

• Glassy dynamics of kinetically constrained models
• Glassy timescale divergence and anomalous coarsening in a kinetically constrained spin chain
• The Asymmetric One-Dimensional Constrained Ising Model
• Monotone cellular automata in a random environment
• Universality results for kinetically constrained spin models in two dimensions
• Sharp metastability threshold for an anisotropic bootstrap percolation model
• The East model: recent results and new progresses
• The second term for two-neighbour bootstrap percolation in two dimensions
• Fredrickson-Andersen one spin facilitated model out of equilibrium
• Refined universality for critical KCM: lower bounds
• Sharp threshold for the FA-2f kinetically constrained model
• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications
• Combinatorics for general kinetically constrained spin models

Cited by in corpus (7)

• Refined universality for critical KCM: lower bounds
• Sharp threshold for the FA-2f kinetically constrained model
• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications
• Refined universality for critical KCM: upper bounds
• Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
• Locality approach to the bootstrap percolation paradox
• Subcritical bootstrap percolation via Toom contours