  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.
