https://doi.org/10.1140/epjs/s11734-023-00804-w
Regular Article
Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model
1
Department of Physics, Boston University, 02215, Boston, MA, USA
2
Santa Fe Institute, 87501, Santa Fe, NM, USA
3
Institut de Physique Théorique, Université Paris-Saclay, CNRS & CEA, 91191, Gif-sur-Yvette, France
Received:
23
November
2022
Accepted:
24
February
2023
Published online:
20
April
2023
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.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
