The Luttinger-Tisza method

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The Luttinger-Tisza method and generalizations of this method for determining the minimum energy spin arrangement in a crystal subject to certain strong conditions are reviewed. It is shown that one can always replace the strong conditions by a set of additional conditions which in the simplest cases is identical with the single weak condition introduced in the Luttinger-Tisza method. A general method of calculating the minimum energy spin arrangement, based on the space group symmetry of the magnetic atom arrangements, is given, and the method of Niemeyer, based on permutation groups, is shown to be equivalent to this method. It is also known that the Luttinger-Tisza conjecture concerning the periodicity of the minimum energy spin arrangement is equivalent to a sufficient, but not necessary, condition for a minimum of the energy.

Original languageEnglish (US)
Pages (from-to)205-219
Number of pages15
JournalPhysica
Volume77
Issue number2
DOIs
StatePublished - Oct 15 1974

Fingerprint

Atoms
Crystals

All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Litvin, Daniel Bernard. / The Luttinger-Tisza method. In: Physica. 1974 ; Vol. 77, No. 2. pp. 205-219.
@article{57c097acc8024865b629fb252db19fdf,
title = "The Luttinger-Tisza method",
abstract = "The Luttinger-Tisza method and generalizations of this method for determining the minimum energy spin arrangement in a crystal subject to certain strong conditions are reviewed. It is shown that one can always replace the strong conditions by a set of additional conditions which in the simplest cases is identical with the single weak condition introduced in the Luttinger-Tisza method. A general method of calculating the minimum energy spin arrangement, based on the space group symmetry of the magnetic atom arrangements, is given, and the method of Niemeyer, based on permutation groups, is shown to be equivalent to this method. It is also known that the Luttinger-Tisza conjecture concerning the periodicity of the minimum energy spin arrangement is equivalent to a sufficient, but not necessary, condition for a minimum of the energy.",
author = "Litvin, {Daniel Bernard}",
year = "1974",
month = "10",
day = "15",
doi = "10.1016/0031-8914(74)90257-2",
language = "English (US)",
volume = "77",
pages = "205--219",
journal = "Physica",
issn = "0031-8914",
publisher = "North-Holland Publ Co",
number = "2",

}

The Luttinger-Tisza method. / Litvin, Daniel Bernard.

In: Physica, Vol. 77, No. 2, 15.10.1974, p. 205-219.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The Luttinger-Tisza method

AU - Litvin, Daniel Bernard

PY - 1974/10/15

Y1 - 1974/10/15

N2 - The Luttinger-Tisza method and generalizations of this method for determining the minimum energy spin arrangement in a crystal subject to certain strong conditions are reviewed. It is shown that one can always replace the strong conditions by a set of additional conditions which in the simplest cases is identical with the single weak condition introduced in the Luttinger-Tisza method. A general method of calculating the minimum energy spin arrangement, based on the space group symmetry of the magnetic atom arrangements, is given, and the method of Niemeyer, based on permutation groups, is shown to be equivalent to this method. It is also known that the Luttinger-Tisza conjecture concerning the periodicity of the minimum energy spin arrangement is equivalent to a sufficient, but not necessary, condition for a minimum of the energy.

AB - The Luttinger-Tisza method and generalizations of this method for determining the minimum energy spin arrangement in a crystal subject to certain strong conditions are reviewed. It is shown that one can always replace the strong conditions by a set of additional conditions which in the simplest cases is identical with the single weak condition introduced in the Luttinger-Tisza method. A general method of calculating the minimum energy spin arrangement, based on the space group symmetry of the magnetic atom arrangements, is given, and the method of Niemeyer, based on permutation groups, is shown to be equivalent to this method. It is also known that the Luttinger-Tisza conjecture concerning the periodicity of the minimum energy spin arrangement is equivalent to a sufficient, but not necessary, condition for a minimum of the energy.

UR - http://www.scopus.com/inward/record.url?scp=34547835637&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547835637&partnerID=8YFLogxK

U2 - 10.1016/0031-8914(74)90257-2

DO - 10.1016/0031-8914(74)90257-2

M3 - Article

AN - SCOPUS:34547835637

VL - 77

SP - 205

EP - 219

JO - Physica

JF - Physica

SN - 0031-8914

IS - 2

ER -