  We consider in parallel three one-dimensional spin models with kinetic
constraints: the paramagnetic constrained Ising chain, the ferromagnetic Ising
chain with constrained Glauber dynamics, and the same chain with constrained
Kawasaki dynamics. At zero temperature the dynamics of these models is fully
irreversible, leading to an exponentially large number of blocked states. Using
a mapping of these spin systems onto sequential adsorption models of,
respectively, monomers, dimers, and hollow trimers, we present exact results on
the statistics of blocked states. We determine the distribution of their energy
or magnetization, and in particular the large-deviation function describing its
exponentially small tails. The spin and energy correlation functions are also
determined. The comparison with an approach based on a priori statistics
reveals systematic discrepancies with the Edwards hypothesis, concerning in
particular the fall-off of correlations.
