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
Cites
Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet
Holstein, T. D., & Primakoff, H. (1940) · Physical Review · doi:10.1103/physrev.58.1098 · Cited by 4,063
Beitrag zur Theorie des Ferromagnetismus
Ising, E. (1925) · Zeitschrift für Physik · doi:10.1007/bf02980577 · Cited by 3,871
An Approximate Quantum Theory of the Antiferromagnetic Ground State
Anderson, P. W. (1952) · Physical Review · doi:10.1103/physrev.86.694 · Cited by 1,337
The Spin-Wave Theory of Antiferromagnetics
Kubo, R. (1952) · Physical Review · doi:10.1103/physrev.87.568 · Cited by 724
Limits on the Energy of the Antiferromagnetic Ground State
Anderson, P. W. (1951) · Physical Review · doi:10.1103/physrev.83.1260 · Cited by 151
Antiferromagnetism by the Spin Wave Method I: The Energy Levels
Ziman, J. M. (1952) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/65/7/309 · Cited by 70
The lowest energy state of a linear antiferromagnetic chain
Kasteleijn, P. W. (1952) · Physica · doi:10.1016/s0031-8914(52)80273-3 · Cited by 68
The Spin-Wave Theory as a Variational Method and Its Application to Antiferromagnetism
Kubo, R. (1953) · Reviews of Modern Physics · doi:10.1103/revmodphys.25.344 · Cited by 61
Lidiard, A. B. (1954) · Reports on Progress in Physics · doi:10.1088/0034-4885/17/1/307 · Cited by 61
Antiferromagnetism by the Spin Wave Method III: Application to more Complex Systems
Ziman, J. M. (1953) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/66/1/313 · Cited by 28
Antiferromagnetism by the Spin Wave Method II: Magnetic Properties
Ziman, J. M. (1952) · Proceedings of the Physical Society Section A · doi:10.1088/0370-1298/65/7/310 · Cited by 21
Flagged first, then by citations
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
- Peierls R. E., 1936, Proc. Roy, Soc. A, 154, 207
- Van Vleck J. H., 1941, J, Chem. Phys., 9, 85
- Van Vleck J. H., 1945, Rev. Mod. Phys., 17, 25
Cited by
Sorted by citations
Linear Magnetic Chains with Anisotropic Coupling
Bonner, J. C., & Fisher, M. E. (1964) · Physical Review · doi:10.1103/physrev.135.a640 · Cited by 2,497
Zhou, Y., Kanoda, K., & Ng, T. K. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.025003 · Cited by 1,486
The spin-½ Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides
Manousakis, E. (1991) · Reviews of Modern Physics · doi:10.1103/revmodphys.63.1 · Cited by 1,252
Aspuru-Guzik, A., & Walther, P. (2012) · Nature Physics · doi:10.1038/nphys2253 · Cited by 952
“In addition to the superior level of quantum control, photonic quantum simulators allow the use of quantum interference at beamsplitters which can lead to interesting photon-entanglement that corresponds to ground states of correlated chemical or solid-state systems 56 .”
Exact solution of an S =1/2 Heisenberg antiferromagnetic chain with long-ranged interactions
Shastry, B. S. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.639 · Cited by 769
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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