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Kinetically constrained models are a class of models in statistical mechanics which were introduced by physicists to model the behavior of glass. They are models of configurations on graphs in which each vertex of the graph is either at state 0 or 1, and can change state only when a constraint of the form “there are enough zeroes around the vertex” is satisfied. There is an infinity of possible constraints, and the properties of a model depend sharply on the choice of its constraint. Therefore a very important question is that of universality: can this infinity of models be sorted into a finite number of classes according to their behavior? Previous works already showed that when the base graph is Z², the models must be divided into three families: supercritical, critical and subcritical, but that inside each of these families, several behaviors can occur, thus an even more precise universality classification is needed. In this talk, we present the universality classification of the particularly interesting critical family.