  The Ising chain with kinetic constraints provides many examples of totally
irreversible zero-temperature dynamics leading to metastability with an
exponentially large number of attractors. In most cases, the constrained
zero-temperature dynamics can be mapped onto a model of random sequential
adsorption. We provide a brief didactic review, based on the example of the
constrained Glauber-Ising chain, of the exact results on the dynamics of these
models and on their attractors that have been obtained by means of the above
mapping. The Riviera model introduced recently by Puljiz et al. behaves
similarly to the kinetically constrained Ising chains. This totally
irreversible deposition model however does not enjoy the shielding property
characterising models of random sequential adsorption. It can therefore neither
be mapped onto such a model nor (in all likelihood) be solved by analytical
means. We present a range of novel results on the attractors of the Riviera
model, obtained by means of an exhaustive enumeration for smaller systems and
of extensive simulations for larger ones, and put these results in perspective
with the exact ones which are available for kinetically constrained Ising
chains.
