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Metastability effects in bootstrap percolation
Open accessAbstract
Bootstrap percolation models, or equivalently certain types of cellular automata, exhibit interesting finite-volume effects. These are studied at a rigorous level. The authors find that for an initial configuration obtained by placing particles independently with probability p<<1, at sites of Z d (d>or=2), the density of the 'bootstrapped' (final) configurations in the sequence of cubes (-L/2, L/2) d typically undergoes an abrupt transition, as L is increased, from being close to 0 to the value 1. With L fixed at a large value, the mean final density as a function of p changes from 0 to 1 around a value which varies only slowly with L-the pertinent parameter being lambda =p 1 (d-1)/ln L. The driving mechanism is the capture of a 'critical droplet'. This behaviour is analogous to the decay of a metastable state near a first-order phase transition, for which the analysis offers some suggestive ideas.
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Citations
Cites
Bootstrap percolation on a Bethe lattice
Chalupa, J., Leath, P. L., & Reich, G. R. (1979) · Journal of Physics C: Solid State Physics · doi:10.1088/0022-3719/12/1/008 · Cited by 572
Cited by
Critical phenomena in complex networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220
k-Core Organization of Complex Networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.040601 · Cited by 709
Recent advances in percolation theory and its applications
Saberi, A. A. (2015) · Physics Reports · doi:10.1016/j.physrep.2015.03.003 · Cited by 438
Kob, W., & Andersen, H. C. (1993) · Physical Review E · doi:10.1103/physreve.48.4364 · Cited by 301
Topological data analysis of contagion maps for examining spreading processes on networks
Taylor, D., Klimm, F., Harrington, H. A., Kramár, M., Mischaikow, K., Porter, M. A., & Mucha, P. J. (2015) · Nature Communications · doi:10.1038/ncomms8723 · Cited by 148
Metadata
- Authors
- Aizenman, M., & Lebowitz, J. L.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1988-10-07
- Volume
- 21
- Issue
- 19
- Pages
- 3801-3813
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W1972354222
- Cited by
- 287
- References
- 1
- FWCI
- 9.62
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Aizenman, M., & Lebowitz, J. L. (1988). Metastability effects in bootstrap percolation. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/21/19/017
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
