Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model

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 characterizing 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 through an exhaustive enumeration for smaller systems and of extensive simulations for larger ones, and put these results into perspective with the exact ones which are available for kinetically constrained Ising chains.