The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Antiferromagnetism
Abstract
The ground state of a lattice with one electron per atom and antiferromagnetic interactions between nearest neighbours only is examined by a variational method similar in principle to the treatments by Hulthén (1938) and Kasteleijn (1952) of the linear-chain problem. The calculation involves a statistical problem which is shown to be exactly equivalent to the Ising ferromagnetic problem. This cannot be solved exactly, except in the one-dimensional case, and so the Bethe–Peierls method is used to solve it approximately. In complete contradiction to the Kubo (1953) variational calculation it is concluded that all lattices have disordered ground states. The energy differences between ordered and disordered states are small and so the nature of the ground state is likely to be sensitive to small additional ordering forces.
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“Based on Marshall's theorem[35] and its extension[36] the absolute ground state has total spin zero ( S 2 = 0 ) for N spins on a bipartite lattice with nearest-neighbor antiferromagnetic Heisenberg-type interactions.”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [35]
Citations
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Research works printed but not linked: 6
- Bethe H. A., 1931, Z, Phys., 71, 694
- Bethe H. A., 1935, Proc. Roy, Soc. A, 150, 552
- Marshall W., 1955, Proc. Roy, Soc. A, 232, 69
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- Van Vleck J. H., 1941, J, Chem. Phys., 9, 85
- Van Vleck J. H., 1945, Rev. Mod. Phys., 17, 25
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Metadata
- Authors
- Marshall, W.
- Affiliations
- University of Birmingham (GB)
- Corresponding author
- Marshall, W.
- Venue
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1955-10-11
- Volume
- 232
- Issue
- 1188
- Pages
- 48-68
- ISSN
- 0080-4630 (ISSN-L)
- 2053-9169
- OpenAlex
- W4250463753
- Cited by
- 444
- References
- 11
- Citations by year
- 2026: 8 · 2025: 17 · 2024: 13 · 2023: 15 · 2022: 12 · 2021: 15 · 2020: 15 · 2019: 11 · 2018: 13 · 2017: 9 · 2016: 8 · 2015: 12 · 2014: 13 · 2013: 7 · 2012: 11
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society of London A Mathematical and Physical Sciences (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- antiferromagnetism, ground state, Ising model, variational methods, disordered ground state, lattice spin systems
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