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The Spherical Model of a Ferromagnet
Abstract
A mathematical model, the spherical model, of a ferromagnet is described. The model is a generalization of the Ising model; and one-, two-, and three-dimensional lattices of infinite extent can be extensively discussed. A three-dimensional lattice shows ferromagnetic behavior and provides a statistical model of the Weiss phenomenological theory. The limiting free energy appears in a form which contains two of the essential features of the exactly known Ising model results in one and two dimensions. This suggests the probable form of the limiting free energy for the three-dimensional Ising model. A simplified model, the Gaussian model, is briefly discussed because this model also contains some of the significant features of the Ising model. However, the Gaussian model, unlike the spherical model, is not defined for all temperatures.
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Citations
Cited by
Theory of the condensation point
Langer, J. S. (1967) · Annals of Physics · doi:10.1016/0003-4916(67)90200-x · Cited by 1,311
Universality classes in nonequilibrium lattice systems
Ódor, G. (2004) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.663 · Cited by 835
Spontaneous breakdown of continuous symmetries near two dimensions
Brézin, E., & Zinn-Justin, J. (1976) · Physical Review B · doi:10.1103/physrevb.14.3110 · Cited by 599
Spherical Model of a Spin-Glass
Kosterlitz, J. M., Thouless, D. J., & Jones, R. C. (1976) · Physical Review Letters · doi:10.1103/physrevlett.36.1217 · Cited by 375
Condensation of the Ideal Bose Gas as a Cooperative Transition
Gunton, J. D., & Buckingham, M. J. (1968) · Physical Review · doi:10.1103/physrev.166.152 · Cited by 138
Metadata
- Authors
- Berlin, T. H., & Kac, M.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1952-06-15
- Volume
- 86
- Issue
- 6
- Pages
- 821-835
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2088593317
- Cited by
- 1,027
- References
- 0
- FWCI
- 2.13
- Type
- journal article
- Language
- en
- Open access
- closed
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- Berlin, T. H., & Kac, M. (1952). The Spherical Model of a Ferromagnet. Physical Review. https://doi.org/10.1103/physrev.86.821
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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