The DOI matches its Crossref record.
Some Cluster Size and Percolation Problems
Abstract
The problem of cluster size distribution and percolation on a regular lattice or graph of bonds and sites is reviewed and its applications to dilute ferromagnetism, polymer gelation, etc., briefly discussed. The cluster size and percolation problems are then solved exactly for Bethe lattices (infinite homogeneous Cayley trees) and for a wide class of pseudolattices derived by replacing the bonds and/or sites of a Bethe lattice by arbitrary finite subgraphs. Explicit expressions are given for the critical probability (density), for the mean cluster size, and for the density of infinite clusters. The nature of the critical anomalies is shown to be the same for all lattices discussed; in particular, the density of infinite clusters vanishes as R(p) ≈ C(p−pc) (p≥pc).
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.
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
Cited by
Kirkpatrick, S. (1973) · Reviews of Modern Physics · doi:10.1103/revmodphys.45.574 · Cited by 5,260
Scaling theory of percolation clusters
Stauffer, D. (1979) · Physics Reports · doi:10.1016/0370-1573(79)90060-7 · Cited by 2,365
Sahimi, M. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.1393 · Cited by 1,082
Percolation and conductivity: A computer study. I
Pike, G. E., & Seager, C. H. (1974) · Physical Review B · doi:10.1103/physrevb.10.1421 · Cited by 1,031
Essam, J. W. (1980) · Reports on Progress in Physics · doi:10.1088/0034-4885/43/7/001 · Cited by 1,018
Self-citation
Metadata
- Authors
- Fisher, M. E., & Essam, J. W.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1961-07-01
- Volume
- 2
- Issue
- 4
- Pages
- 609-619
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2032411420
- Cited by
- 564
- References
- 0
- FWCI
- 2.06
- Type
- journal article
- Language
- en
- Open access
- closed
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: Some Cluster Size and Percolation Problems. https://app.cochat.ai/papers/10.1063/1.1703745
- The paper
- Fisher, M. E., & Essam, J. W. (1961). Some Cluster Size and Percolation Problems. Journal of Mathematical Physics. https://doi.org/10.1063/1.1703745
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
