Kinetically constrained spin models: a short survey

Kinetically constrained models (KCMs) are interacting particle systems introduced in the '80s by condensed matter physicists to have accessible stochastic models with glassy-type dynamics. The key mechanism behind the complex evolution of these otherwise simple models is the so-called dynamical facilitation, a feature embedded into the models via appropriate kinetic constraints. KCMs are tightly related to bootstrap percolation, a widely studied monotone cellular automaton, and they have recently inspired the construction of quantum spin chains to explore many-body localization in the absence of disorder and ergodicity breaking transition. In the first half of this survey, I will review some of the general features of KCMs and the detailed behaviour of three of the most popular models. In the second half, I will focus on the KCMs counterpart of the famous "universality problem" for two-dimensional bootstrap percolation, a broad research program in extremal probabilistic combinatorics