The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Bootstrap percolation on a Bethe lattice
Open accessAbstract
A new percolation problem is posed which can exhibit a first-order transition. In bootstrap percolation, sites on an empty lattice are first randomly occupied, and then all occupied sites with less than a given number m of occupied neighbours are successively removed until a stable configuration is reached. On any lattice for sufficiently large m, the ensuing clusters can only be infinite. On a Bethe lattice for m>or=3, the fraction of the lattice occupied by infinite clusters discontinuously jumps from zero at the percolation threshold. From an analysis of stable and metastable ground states of the dilute Blume-Capel model (1966), it is concluded that effects like bootstrap percolation may occur in some real magnets.
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“One such approach sets a threshold for a node failure if its number of functional (non-failed) neighbors is below this threshold27,28.”
From Mitigation of cascading failures in complex networks (2020) · cites this paper as [27]
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Citations
Cites
Theory of the First-Order Magnetic Phase Change in U O 2
Blume, M. (1966) · Physical Review · doi:10.1103/physrev.141.517 · Cited by 1,070
Capel, H. W. (1966) · Physica · doi:10.1016/0031-8914(66)90027-9 · Cited by 931
Statistical theory of nucleation, condensation and coagulation
Binder, K., & Stauffer, D. (1976) · Advances In Physics · doi:10.1080/00018737600101402 · Cited by 700
Some Cluster Size and Percolation Problems
Fisher, M. E., & Essam, J. W. (1961) · Journal of Mathematical Physics · doi:10.1063/1.1703745 · Cited by 568
Magnetic Ordering Properties of Rare-Earth Ions in Strong Cubic Crystal Fields
Trammell, G. T. (1963) · Physical Review · doi:10.1103/physrev.131.932 · Cited by 258
Weak Interactions and Eötvös Experiments
Haugan, M. P., & Will, C. M. (1976) · Physical Review Letters · doi:10.1103/physrevlett.37.1 · Cited by 149
Skal, A. S., & Shklovskii, B. I. (1975) · Cited by 145
Transition from Van Vleck Paramagnetism to Induced Antiferromagnetism in Tb ζ Y 1 − ζ Sb
Cooper, B. R., & Vogt, O. (1970) · Physical review. B, Solid state · doi:10.1103/physrevb.1.1218 · Cited by 81
Monte Carlo computer experiments on critical phenomena and metastable states
Binder, K. (1974) · Advances In Physics · doi:10.1080/00018737400101441 · Cited by 72
Clusters, metastability, and nucleation: Kinetics of first-order phase transitions
Kalos, M. H., Lebowitz, J. L., Penrose, O., et al. (1978) · Journal of Statistical Physics · doi:10.1007/bf01014669 · Cited by 49
Research works printed but not linked: 6
- Chalupa J, 1978, Solid St. Commun.
- Chalupa J, 1978, Solid St. Commun.
- Reich G R, 1978, J. Stat. Phys.
- Skal A, 1974, Fiz. Tekh. Poluprov., 8, 1586
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Cited by
Sorted by citations
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
Topological Strata of Weighted Complex Networks
Petri, G., Scolamiero, M., Donato, I., & Vaccarino, F. (2013) · PLoS ONE · doi:10.1371/journal.pone.0066506 · Cited by 214
Mitigation of cascading failures in complex networks
Smolyak, A., Levy, O., Vodenska, I., Buldyrev, S., & Havlin, S. (2020) · Scientific Reports · doi:10.1038/s41598-020-72771-4 · Cited by 67
Metadata
- Authors
- Chalupa, J., Leath, P. L., & Reich, G. R.
- Affiliations
- Rutgers, The State University of New Jersey (US)
- Venue
- Journal of Physics C: Solid State Physics
- Publisher
- IOP Publishing
- Published
- 1979-01-14
- Volume
- 12
- Issue
- 1
- Pages
- L31-L35
- ISSN
- 0022-3719 (ISSN-L)
- OpenAlex
- W2027508917
- Semantic Scholar
- f3beda297ffe8ad4adac9b252f328a93bcab9e5c
- Cited by
- 572
- References
- 13
- Citations by year
- 2026: 8 · 2025: 20 · 2024: 19 · 2023: 19 · 2022: 45 · 2021: 24 · 2020: 24 · 2019: 27 · 2018: 49 · 2017: 34 · 2016: 40 · 2015: 34 · 2014: 32 · 2013: 32 · 2012: 20
- FWCI
- 2.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics C Solid State Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Physical Sciences › Mathematics › Mathematical Physics › p-Adic Analysis and Mathematical Physics
- Keywords
- bootstrap percolation, Bethe lattice, first-order phase transition, percolation threshold, infinite cluster, metastable ground state, spin glass
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