On the Absence of Ferromagnetism in Typical 2D Ferromagnets

Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at lon...
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Gespeichert in:

Autor*in:	Biskup, Marek [verfasserIn] Chayes, Lincoln Kivelson, Steven A.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2007

Schlagwörter:	Gibbs Measure Spontaneous Magnetization Gibbs State Striped State Peierls Argument

Anmerkung:	© M. Biskup, L. Chayes and S.A. Kivelson 2007

Übergeordnetes Werk:	Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 274(2007), 1 vom: 16. Mai, Seite 217-231
Übergeordnetes Werk:	volume:274 ; year:2007 ; number:1 ; day:16 ; month:05 ; pages:217-231

Links:	Volltext

DOI / URN:	10.1007/s00220-007-0260-0

Katalog-ID:	OLC2038891842

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650		4	\|a Gibbs Measure
650		4	\|a Spontaneous Magnetization
650		4	\|a Gibbs State
650		4	\|a Striped State
650		4	\|a Peierls Argument
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allfields_unstemmed	10.1007/s00220-007-0260-0 doi (DE-627)OLC2038891842 (DE-He213)s00220-007-0260-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut On the Absence of Ferromagnetism in Typical 2D Ferromagnets 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S.A. Kivelson 2007 Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur. Gibbs Measure Spontaneous Magnetization Gibbs State Striped State Peierls Argument Chayes, Lincoln aut Kivelson, Steven A. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 274(2007), 1 vom: 16. Mai, Seite 217-231 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:274 year:2007 number:1 day:16 month:05 pages:217-231 https://doi.org/10.1007/s00220-007-0260-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 274 2007 1 16 05 217-231
allfieldsGer	10.1007/s00220-007-0260-0 doi (DE-627)OLC2038891842 (DE-He213)s00220-007-0260-0-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut On the Absence of Ferromagnetism in Typical 2D Ferromagnets 2007 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S.A. Kivelson 2007 Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur. Gibbs Measure Spontaneous Magnetization Gibbs State Striped State Peierls Argument Chayes, Lincoln aut Kivelson, Steven A. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 274(2007), 1 vom: 16. Mai, Seite 217-231 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:274 year:2007 number:1 day:16 month:05 pages:217-231 https://doi.org/10.1007/s00220-007-0260-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 274 2007 1 16 05 217-231
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author	Biskup, Marek
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author_browse	Biskup, Marek Chayes, Lincoln Kivelson, Steven A.
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title_sort	on the absence of ferromagnetism in typical 2d ferromagnets
title_auth	On the Absence of Ferromagnetism in Typical 2D Ferromagnets
abstract	Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur. © M. Biskup, L. Chayes and S.A. Kivelson 2007
abstractGer	Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur. © M. Biskup, L. Chayes and S.A. Kivelson 2007
abstract_unstemmed	Abstract We consider the Ising systems in d dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions that decay with power s of the distance. The physical context of such models is discussed; primarily this is d = 2 and s = 3 where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above d and does not exceed d + 1, then for all temperatures the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding d + 1 (with d ≥ 2) magnetic order can occur. © M. Biskup, L. Chayes and S.A. Kivelson 2007
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title_short	On the Absence of Ferromagnetism in Typical 2D Ferromagnets
url	https://doi.org/10.1007/s00220-007-0260-0
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up_date	2024-07-03T20:45:01.823Z
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