Universality for critical KCM: finite number of stable directions

TL;DR

This paper proves that for critical kinetically constrained models with a finite number of stable directions, the divergence of infection time matches bootstrap percolation, establishing a universal behavior and identifying the key mechanism as hierarchical East-like motions.

Contribution

It demonstrates the full universality partition for critical KCM with finite stable directions and identifies the hierarchical East-like motions as the main governing mechanism.

Findings

Divergence of infection time matches bootstrap percolation in the finite stable directions case.

Established the universality partition for critical KCM.

Identified hierarchical East-like motions as the key mechanism.

Abstract

In this paper we consider kinetically constrained models (KCM) on $\mathbb Z^2$ with general update families $\mathcal U$. For $\mathcal U$ belonging to the so-called "critical class" our focus is on the divergence of the infection time of the origin for the equilibrium process as the density of the facilitating sites vanishes. In a recent paper Mar\^ech\'e and two of the present authors proved that if $\mathcal U$ has an infinite number of "stable directions", then on a doubly logarithmic scale the above divergence is twice the one in the corresponding $\mathcal U$-bootstrap percolation. Here we prove instead that, contrary to previous conjectures, in the complementary case the two divergences are the same. In particular, we establish the full universality partition for critical $\mathcal U$. The main novel contribution is the identification of the leading mechanism governing the motion of infected critical droplets. It consists of a peculiar hierarchical combination of mesoscopic East-like motions.