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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source says what the claim attributes to it.
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
- Skal A, 1975, Sov. Phys.-Semicond., 8, 1029
- Young A P, 1978, Bull. Am. Phys. Soc., 23, 204
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Bootstrap percolation on a Bethe lattice. https://app.cochat.ai/papers/10.1088/0022-3719/12/1/008
- The paper
- Chalupa, J., Leath, P. L., & Reich, G. R. (1979). Bootstrap percolation on a Bethe lattice. Journal of Physics C: Solid State Physics. https://doi.org/10.1088/0022-3719/12/1/008
