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A Theory of Cooperative Phenomena
Abstract
A new method of approximation for order-disorder phenomena is developed. In Sec. A, the method is explained for the one-dimensional Ising lattice. Sections B and C cover the approximations already known, such as those of Bethe (Sec. B) and of Kramers-Wannier (Sec. C), which are shown to be derived as special cases of the method with suitable choices of variables. In Sec. D, an improved treatment is explained for the three-dimensional simple cubic Ising lattice. This approximation is found to agree with the rigorous expansion of the partition function up to the fourth moment by Kirkwood's moment method, so far as the disordered state is concerned. In Sec. E the general formula for the entropy is given. In Sec. H an improved treatment of the face-centered lattice (Ising model) is given.
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Cited by
Georges, A., Kotliar, G., Krauth, W., & Rozenberg, M. J. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.13 · Cited by 6,901
Margolin, A. A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Favera, R. D., & Califano, A. (2006) · BMC Bioinformatics · doi:10.1186/1471-2105-7-s1-s7 · Cited by 2,420
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
What is "liquid"? Understanding the states of matter
Barker, J. A., & Henderson, D. (1976) · Reviews of Modern Physics · doi:10.1103/revmodphys.48.587 · Cited by 2,104
Hart, G. L. W., Mueller, T., Toher, C., & Curtarolo, S. (2021) · Nature Reviews Materials · doi:10.1038/s41578-021-00340-w · Cited by 703
Metadata
- Authors
- Kikuchi, R.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1951-03-15
- Volume
- 81
- Issue
- 6
- Pages
- 988-1003
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2007995670
- Cited by
- 1,942
- References
- 0
- FWCI
- 6.87
- Type
- journal article
- Language
- en
- Open access
- closed
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