DOI: 10.1098/rspa.1955.0200. Antiferromagnetism

Antiferromagnetism

10.1098/rspa.1955.0200

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

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.

Bibliography

Antiferromagnetism. (1955). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 232(1188), 48â68.

Authors 0

None

References 18 Referenced 391

10.1103/PhysRev.83.1260
10.1103/PhysRev.86.694
{'key': 'p_3', 'first-page': '694', 'article-title': 'Z', 'volume': '71', 'author': 'Bethe H. A.', 'year': '1931', 'journal-title': 'Phys.'} / Phys. / Z by Bethe H. A. (1931)
{'key': 'p_4', 'first-page': '552', 'article-title': 'Proc. Roy', 'volume': '150', 'author': 'Bethe H. A.', 'year': '1935', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Bethe H. A. (1935)
10.1103/PhysRev.58.1098
Hulthen L. 1938 Ark. M at. Astr. Fys. 26 A no. 1.
10.1007/BF02980577
Kasteleijn P. W. 1952 Physica 18 104. (10.1016/S0031-8914(52)80273-3)
10.1103/PhysRev.87.568
10.1103/RevModPhys.25.344
10.1088/0034-4885/17/1/307
{'key': 'p_12', 'first-page': '69', 'article-title': 'Proc. Roy', 'volume': '232', 'author': 'Marshall W.', 'year': '1955', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Marshall W. (1955)
{'key': 'p_13', 'first-page': '207', 'article-title': 'Proc. Roy', 'volume': '154', 'author': 'Peierls R. E.', 'year': '1936', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Peierls R. E. (1936)
{'key': 'p_14', 'first-page': '85', 'article-title': 'J', 'volume': '9', 'author': 'Van Vleck J. H.', 'year': '1941', 'journal-title': 'Chem. Phys.'} / Chem. Phys. / J by Van Vleck J. H. (1941)
{'key': 'p_15', 'first-page': '25', 'volume': '17', 'author': 'Van Vleck J. H.', 'year': '1945', 'journal-title': 'Rev. Mod. Phys.'} / Rev. Mod. Phys. by Van Vleck J. H. (1945)
10.1088/0370-1298/65/7/309
10.1088/0370-1298/65/7/310
10.1088/0370-1298/66/1/313

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 5:03 p.m.)
Deposited	4 years, 6 months ago (Feb. 19, 2021, 7:57 a.m.)
Indexed	6 days, 8 hours ago (Aug. 23, 2025, 9:57 p.m.)
Issued	69 years, 10 months ago (Oct. 11, 1955)
Published	69 years, 10 months ago (Oct. 11, 1955)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	69 years, 10 months ago (Oct. 11, 1955)

Funders 0

None

BibTeX

@article{1955, volume={232}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1955.0200}, DOI={10.1098/rspa.1955.0200}, number={1188}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1955}, month=oct, pages={48–68} }

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