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Antiferromagnetism. The Triangular Ising Net
Abstract
In this paper the statistical mechanics of a two-dimensionally infinite set of Ising spins is worked out for the case in which they form either a triangular or a honeycomb arrangement. Results for the honeycomb and the ferromagnetic triangular net differ little from the published ones for the square net (Curie point with logarithmically infinite specific heat). The triangular net with antiferromagnetic interaction is a sample case of antiferromagnetism in a non-fitting lattice. The binding energy comes out to be only one-third of what it is in the ferromagnetic case. The entropy at absolute zero is finite; it equals $S(0)=R\frac{2}{\ensuremath{\pi}}\ensuremath{\int}{0}^{\frac{\ensuremath{\pi}}{3}}\mathrm{ln}(2cos\ensuremath{\omega})d\ensuremath{\omega}=0.3383R$The system is disordered at all temperatures and possesses no Curie point.
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Citations
Cites
Beitrag zur Theorie des Ferromagnetismus
Ising, E. (1925) · Zeitschrift für Physik · doi:10.1007/bf02980577 · Cited by 3,871
Cited by
Spin liquids in frustrated magnets
Balents, L. (2010) · Nature · doi:10.1038/nature08917 · Cited by 4,316
Wu, F. Y. (1982) · Reviews of Modern Physics · doi:10.1103/revmodphys.54.235 · Cited by 3,570
Gardner, J. S., Gingras, M. J. P., & Greedan, J. E. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.53 · Cited by 1,372
Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
Scholl, P., Schuler, M., Williams, H. J., Eberharter, A. A., Barredo, D., Schymik, K.-N., Lienhard, V., Henry, L.-P., Lang, T. C., Lahaye, T., et al. (2021) · Nature · doi:10.1038/s41586-021-03585-1 · Cited by 688
Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices
Struck, J., Ölschläger, C., Le Targat, R., Soltan-Panahi, P., Eckardt, A., Lewenstein, M., Windpassinger, P., & Sengstock, K. (2011) · Science · doi:10.1126/science.1207239 · Cited by 669
Metadata
- Authors
- Wannier, G. H.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1950-07-15
- Volume
- 79
- Issue
- 2
- Pages
- 357-364
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2031392878
- Cited by
- 1,426
- References
- 1
- FWCI
- 2.72
- Type
- journal article
- Language
- en
- Open access
- closed
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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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