The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
Two-Dimensional Ising Model as a Soluble Problem of Many Fermions
Abstract
The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble and shows a phase transition. Although the exact solution in the absence of an external magnetic field was first given almost twenty years ago in a famous paper by Onsager1 using the theory of Lie algebras, the flow of papers on both approximate and exact methods has remained strong to this day.2 One reason for this has been the interest in testing approximate methods on an exactly soluble problem. A second reason, no doubt, has been the considerable formidability of the Onsager method. The simplification achieved by Bruria Kaufman3 using the theory of spinor representations has diminished, but not removed, the reputation of the Onsager approach for incomprehensibility, while the subsequent application of this method by Yang4 to the calculation of the spontaneous magnetization has, if anything, helped to restore this reputation.
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Citations
Cites
Bardeen, J., Cooper, L. N., & Schrieffer, J. R. (1957) · Physical Review · doi:10.1103/physrev.108.1175 · Cited by 13,213
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
Two soluble models of an antiferromagnetic chain
Lieb, E., Schultz, T., & Mattis, D. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90115-4 · Cited by 4,280
Self-citation�ber das Paulische �quivalenzverbot
Jordan, P., & Wigner, E. (1928) · Zeitschrift f�r Physik · doi:10.1007/bf01331938 · Cited by 2,597
Toeplitz Forms and Their Applications
Grenander, U., Szegö, G., & Kac, M. (1958) · Physics Today · doi:10.1063/1.3062237 · Cited by 1,840
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
Random-Phase Approximation in the Theory of Superconductivity
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.112.1900 · Cited by 1,381
On a new method in the theory of superconductivity
Bogoljubov, N. N. (1958) · Il Nuovo Cimento · doi:10.1007/bf02745585 · Cited by 1,324
The Spontaneous Magnetization of a Two-Dimensional Ising Model
Yang, C. N. (1952) · Physical Review · doi:10.1103/physrev.85.808 · Cited by 1,221
About the Pauli exclusion principle
Jordán, P., & Wigner, E. P. (1928) · Cited by 951
Cited by
An introduction to lattice gauge theory and spin systems
Kogut, J. B. (1979) · Reviews of Modern Physics · doi:10.1103/revmodphys.51.659 · Cited by 2,029
History of the Lenz-Ising Model
BRUSH, S. G. (1967) · Reviews of Modern Physics · doi:10.1103/revmodphys.39.883 · Cited by 721
Dynamical quantum phase transitions: a review
Heyl, M. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aaaf9a · Cited by 678
Correlations in Ising Ferromagnets. I
Griffiths, R. B. (1967) · Journal of Mathematical Physics · doi:10.1063/1.1705219 · Cited by 485
Quantum Hamiltonian Complexity
Gharibian, S., Huang, Y., Landau, Z., & Shin, S. W. (2015) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000066 · Cited by 144
Metadata
- Authors
- SCHULTZ, T. D., MATTIS, D. C., & LIEB, E. H.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1964-07-01
- Volume
- 36
- Issue
- 3
- Pages
- 856-871
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W2021912944
- Cited by
- 936
- References
- 27
- FWCI
- 4.46
- Type
- journal article
- Language
- en
- Open access
- closed
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- SCHULTZ, T. D., MATTIS, D. C., & LIEB, E. H. (1964). Two-Dimensional Ising Model as a Soluble Problem of Many Fermions. Reviews of Modern Physics. https://doi.org/10.1103/revmodphys.36.856
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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).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
