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Correlations and Spontaneous Magnetization of the Two-Dimensional Ising Model
Abstract
In this paper we rederive, by simpler methods, the Onsager-Kaufman formulas for the correlations and the Onsager formula for the spontaneous magnetization of the rectangular two-dimensional Ising lattice. The Pfaffian approach is used to derive the correlations in terms of Pfaffians, and for the correlations in a row a single Toeplitz determinant is obtained which is proved equivalent to the Onsager-Kaufman result. The spontaneous magnetization is obtained as the limiting value of an infinite Toeplitz determinant and its evaluation is facilitated by use of the generalization of a result first published by Szego.
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Citations
Cited by
Two-Dimensional Ising Model as a Soluble Problem of Many Fermions
SCHULTZ, T. D., MATTIS, D. C., & LIEB, E. H. (1964) · Reviews of Modern Physics · doi:10.1103/revmodphys.36.856 · Cited by 936
History of the Lenz-Ising Model
BRUSH, S. G. (1967) · Reviews of Modern Physics · doi:10.1103/revmodphys.39.883 · Cited by 721
Wu, T. T., McCoy, B. M., Tracy, C. A., & Barouch, E. (1976) · Physical Review B · doi:10.1103/physrevb.13.316 · Cited by 694
Interfacial, Boundary, and Size Effects at Critical Points
Fisher, M. E., & Ferdinand, A. E. (1967) · Physical Review Letters · doi:10.1103/physrevlett.19.169 · Cited by 397
Moore, C., & Mertens, S. (2011) · doi:10.1093/acprof:oso/9780199233212.001.0001 · Cited by 347
Metadata
- Authors
- Montroll, E. W., Potts, R. B., & Ward, J. C.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1963-02-01
- Volume
- 4
- Issue
- 2
- Pages
- 308-322
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2082952025
- Cited by
- 345
- References
- 0
- FWCI
- 2.03
- Type
- journal article
- Language
- en
- Open access
- closed
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- Montroll, E. W., Potts, R. B., & Ward, J. C. (1963). Correlations and Spontaneous Magnetization of the Two-Dimensional Ising Model. Journal of Mathematical Physics. https://doi.org/10.1063/1.1703955
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