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Statistics of the Two-Dimensional Ferromagnet. Part II
Abstract
The study of the two-dimensional Ising model is continued. Its specific heat at the Curie point is investigated. The quantity in question is computed for six successive finite matrix problems and the conclusion is drawn that the specific heat is infinite at the Curie point. A new closed form approximation of the partition function $\ensuremath{\lambda}$ is then developed by using the matrix method in its variational form. The two power series for $\ensuremath{\lambda}$ at extreme temperatures are used as a test for this and various other approximations, and it is found that the new result is a considerable improvement over the existing solutions. Finally it is pointed out that these closed form solutions support our conclusion as to the place and nature of the Curie point transition.
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Cited by
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The density matrix renormalization group for ab initio quantum chemistry
Wouters, S., & Van Neck, D. (2014) · The European Physical Journal D · doi:10.1140/epjd/e2014-50500-1 · Cited by 285
Tensor Network Contractions: Methods and Applications to Quantum Many-Body Systems
Ran, S.-J., Tirrito, E., Peng, C., Chen, X., Tagliacozzo, L., Su, G., & Lewenstein, M. (2020) · Lecture Notes in Physics · doi:10.1007/978-3-030-34489-4 · Cited by 176
Faster methods for contracting infinite two-dimensional tensor networks
Fishman, M. T., Vanderstraeten, L., Zauner-Stauber, V., Haegeman, J., & Verstraete, F. (2018) · Physical Review B · doi:10.1103/physrevb.98.235148 · Cited by 128
Particle-time duality in the kicked Ising spin chain
Akila, M., Waltner, D., Gutkin, B., & Guhr, T. (2016) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/49/37/375101 · Cited by 124
Metadata
- Authors
- Kramers, H. A., & Wannier, G. H.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1941-08-01
- Volume
- 60
- Issue
- 3
- Pages
- 263-276
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W4240736707
- Cited by
- 310
- References
- 0
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kramers, H. A., & Wannier, G. H. (1941). Statistics of the Two-Dimensional Ferromagnet. Part II. Physical Review. https://doi.org/10.1103/physrev.60.263
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