Combinatorics for general kinetically constrained spin models

Abstract

We study the set of possible configurations for a general kinetically constrained model (KCM), a non monotone version of the $\mathcal{U}$-bootstrap percolation cellular automata. We solve a combinatorial question that is a generalization of a problem addressed by Chung, Diaconis and Graham in 2001 for a specific one-dimensional KCM, the East model. Since the general models we consider are in any dimension and lack the oriented character of the East dynamics, we have to follow a completely different route than the one taken by Chung, Diaconis and Graham. Our combinatorial result is used by Marêché, Martinelli and Toninelli to complete the proof of a conjecture put forward by Morris.

13 pages, 6 figures

References in corpus (4)

• Theoretical perspective on the glass transition and amorphous materials
• Glassy dynamics of kinetically constrained models
• Universality results for kinetically constrained spin models in two dimensions
• Exact asymptotics for Duarte and supercritical rooted kinetically constrained models

Cited by in corpus (4)

• Refined universality for critical KCM: lower bounds
• $\mathcal{U}$-bootstrap percolation: critical probability, exponential decay and applications
• Refined universality for critical KCM: upper bounds
• Bisection for kinetically constrained models revisited