The DOI matches its Crossref record; 48 of the 48 references it cites were found in a registry or an index.
History of the Lenz-Ising Model
Abstract
Many physico-chemical systems can be represented more or less accurately by a lattice arrangement of molecules with nearest-neighbor interactions. The simplest and most popular version of this theory is the so-called "Ising model," discussed by Ernst Ising in 1925 but suggested earlier (1920) by Wilhelm Lenz.Major events in the subsequent history of the Lenz-Ising model are reviewed, including early approximate methods of solution, Onsager's exact result for the two-dimensional model, the use of the mathematically equivalent "lattice gas" model to study gas-liquid and liquid-solid phase transitions, and recent progress in determining the singularities of thermodynamic and magnetic properties at the critical point. Not only is there a wide range of possible physical applications of the model, there is also an urgent need for the application of advanced mathematical techniques in order to establish its exact properties, especially in the neighborhood of phase transitions where approximate methods are unreliable.
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Citations
Cites
Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
Onsager, L. (1944) · Physical Review · doi:10.1103/physrev.65.117 · Cited by 6,510
Beitrag zur Theorie des Ferromagnetismus
Ising, E. (1925) · Zeitschrift für Physik · doi:10.1007/bf02980577 · Cited by 3,871
Phase Transition for a Hard Sphere System
Alder, B. J., & Wainwright, T. E. (1957) · The Journal of Chemical Physics · doi:10.1063/1.1743957 · Cited by 2,644
Onsager, L. (1949) · Il Nuovo Cimento · doi:10.1007/bf02780991 · Cited by 2,550
Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
Lee, T. D., & Yang, C. N. (1952) · Physical Review · doi:10.1103/physrev.87.410 · Cited by 2,228
Some generalized order-disorder transformations
Potts, R. B. (1952) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100027419 · Cited by 2,122
Statistics of the Two-Dimensional Ferromagnet. Part I
Kramers, H. A., & Wannier, G. H. (1941) · Physical Review · doi:10.1103/physrev.60.252 · Cited by 1,812
Zur Theorie des Ferromagnetismus
Heisenberg, W. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01328601 · Cited by 1,811
Static Phenomena Near Critical Points: Theory and Experiment
KADANOFF, L. P., GÖTZE, W., HAMBLEN, D., HECHT, R., LEWIS, E. A. S., PALCIAUSKAS, V. V., RAYL, M., SWIFT, J., ASPNES, D., & KANE, J. (1967) · Reviews of Modern Physics · doi:10.1103/revmodphys.39.395 · Cited by 1,617
Scaling laws for ising models near Tc
Kadanoff, L. P. (1966) · Physics Physique Fizika · doi:10.1103/physicsphysiquefizika.2.263 · Cited by 1,608
Cited by
Broadband criticality of human brain network synchronization
Kitzbichler, M. G., Smith, M. L., Christensen, S. R., & Bullmore, E. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000314 · Cited by 527
Quantum simulations with cold trapped ions
Johanning, M., Varón, A. F., & Wunderlich, C. (2009) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/42/15/154009 · Cited by 208
Model of human collective decision-making in complex environments
Carbone, G., & Giannoccaro, I. (2015) · The European Physical Journal B · doi:10.1140/epjb/e2015-60609-0 · Cited by 35
Contact Potential for Structure Prediction of Proteins and Protein Complexes from Potts Model
Anishchenko, I., Kundrotas, P. J., & Vakser, I. A. (2018) · Biophysical Journal · doi:10.1016/j.bpj.2018.07.035 · Cited by 29
Mindstorms in Natural Language-Based Societies of Mind
Zhuge, M., Liu, H., Faccio, F., Ashley, D. R., Csordás, R., Gopalakrishnan, A., Hamdi, A., Hammoud, H. A. A. K., Herrmann, V., Irie, K., et al. (2023) · arXiv · doi:10.48550/arxiv.2305.17066 · Cited by 24
Metadata
- Authors
- BRUSH, S. G.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1967-10-01
- Volume
- 39
- Issue
- 4
- Pages
- 883-893
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2065704711
- Cited by
- 721
- References
- 48
- FWCI
- 0.94
- Type
- journal article
- Language
- en
- Open access
- closed
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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).
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