Long-range order in the XXZ model

Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficien...
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Autor*in:	Nishimori, Hidetoshi [verfasserIn] Kubo, Kenn Ozeki, Yukiyasu Tomita, Yasuhiro Kishi, Tatsuya

Format:	Artikel
Sprache:	Englisch

Erschienen:	1989

Anmerkung:	© Plenum Publishing Corporation 1989

Übergeordnetes Werk:	Enthalten in: Journal of statistical physics - Kluwer Academic Publishers-Plenum Publishers, 1969, 55(1989), 1-2 vom: Apr., Seite 259-277
Übergeordnetes Werk:	volume:55 ; year:1989 ; number:1-2 ; month:04 ; pages:259-277

Links:	Volltext

DOI / URN:	10.1007/BF01042599

Katalog-ID:	OLC2046563697

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520			\|a Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.
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allfields	10.1007/BF01042599 doi (DE-627)OLC2046563697 (DE-He213)BF01042599-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Nishimori, Hidetoshi verfasserin aut Long-range order in the XXZ model 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1989 Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. Kubo, Kenn aut Ozeki, Yukiyasu aut Tomita, Yasuhiro aut Kishi, Tatsuya aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 55(1989), 1-2 vom: Apr., Seite 259-277 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:55 year:1989 number:1-2 month:04 pages:259-277 https://doi.org/10.1007/BF01042599 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2012 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4037 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4323 GBV_ILN_4700 33.00 VZ AR 55 1989 1-2 04 259-277
spelling	10.1007/BF01042599 doi (DE-627)OLC2046563697 (DE-He213)BF01042599-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Nishimori, Hidetoshi verfasserin aut Long-range order in the XXZ model 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1989 Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. Kubo, Kenn aut Ozeki, Yukiyasu aut Tomita, Yasuhiro aut Kishi, Tatsuya aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 55(1989), 1-2 vom: Apr., Seite 259-277 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:55 year:1989 number:1-2 month:04 pages:259-277 https://doi.org/10.1007/BF01042599 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2012 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4037 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4323 GBV_ILN_4700 33.00 VZ AR 55 1989 1-2 04 259-277
allfields_unstemmed	10.1007/BF01042599 doi (DE-627)OLC2046563697 (DE-He213)BF01042599-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Nishimori, Hidetoshi verfasserin aut Long-range order in the XXZ model 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1989 Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. Kubo, Kenn aut Ozeki, Yukiyasu aut Tomita, Yasuhiro aut Kishi, Tatsuya aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 55(1989), 1-2 vom: Apr., Seite 259-277 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:55 year:1989 number:1-2 month:04 pages:259-277 https://doi.org/10.1007/BF01042599 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2012 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4037 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4323 GBV_ILN_4700 33.00 VZ AR 55 1989 1-2 04 259-277
allfieldsGer	10.1007/BF01042599 doi (DE-627)OLC2046563697 (DE-He213)BF01042599-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Nishimori, Hidetoshi verfasserin aut Long-range order in the XXZ model 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1989 Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. Kubo, Kenn aut Ozeki, Yukiyasu aut Tomita, Yasuhiro aut Kishi, Tatsuya aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 55(1989), 1-2 vom: Apr., Seite 259-277 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:55 year:1989 number:1-2 month:04 pages:259-277 https://doi.org/10.1007/BF01042599 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2012 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4037 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4323 GBV_ILN_4700 33.00 VZ AR 55 1989 1-2 04 259-277
allfieldsSound	10.1007/BF01042599 doi (DE-627)OLC2046563697 (DE-He213)BF01042599-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Nishimori, Hidetoshi verfasserin aut Long-range order in the XXZ model 1989 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1989 Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. Kubo, Kenn aut Ozeki, Yukiyasu aut Tomita, Yasuhiro aut Kishi, Tatsuya aut Enthalten in Journal of statistical physics Kluwer Academic Publishers-Plenum Publishers, 1969 55(1989), 1-2 vom: Apr., Seite 259-277 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:55 year:1989 number:1-2 month:04 pages:259-277 https://doi.org/10.1007/BF01042599 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_23 GBV_ILN_32 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2012 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_2192 GBV_ILN_2333 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4036 GBV_ILN_4037 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4323 GBV_ILN_4700 33.00 VZ AR 55 1989 1-2 04 259-277
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author	Nishimori, Hidetoshi
spellingShingle	Nishimori, Hidetoshi ddc 530 bkl 33.00 Long-range order in the XXZ model
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topic_title	530 VZ 33.00 bkl Long-range order in the XXZ model
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title	Long-range order in the XXZ model
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title_full	Long-range order in the XXZ model
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author_browse	Nishimori, Hidetoshi Kubo, Kenn Ozeki, Yukiyasu Tomita, Yasuhiro Kishi, Tatsuya
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title_sort	long-range order in the xxz model
title_auth	Long-range order in the XXZ model
abstract	Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. © Plenum Publishing Corporation 1989
abstractGer	Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. © Plenum Publishing Corporation 1989
abstract_unstemmed	Abstract The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropyΔ(≥0) ifS≥1, and for 0≤Δ<0.29 (XY-like) orΔ>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (Δ≥0) ifS≥3/2; 0≤Δ<0.032 (XY-like) or 0.67<Δ<1.34 (almost isotropic) orΔ>1.80 (Ising-like) ifS=1;Δ>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (Δ=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given. © Plenum Publishing Corporation 1989
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title_short	Long-range order in the XXZ model
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author2	Kubo, Kenn Ozeki, Yukiyasu Tomita, Yasuhiro Kishi, Tatsuya
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