Quantum Spin Systems at Positive Temperature
Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a sim...
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| Autor*in: |
Biskup, Marek [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© M. Biskup, L. Chayes and S. Starr 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 269(2006), 3 vom: 15. Nov., Seite 611-657 |
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| Übergeordnetes Werk: |
volume:269 ; year:2006 ; number:3 ; day:15 ; month:11 ; pages:611-657 |
| Links: |
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| DOI / URN: |
10.1007/s00220-006-0135-9 |
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| Katalog-ID: |
OLC2038890617 |
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| 520 | |a Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. | ||
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| 650 | 4 | |a Coherent State | |
| 650 | 4 | |a Positive Temperature | |
| 650 | 4 | |a Gibbs State | |
| 650 | 4 | |a Quantum Spin System | |
| 700 | 1 | |a Chayes, Lincoln |4 aut | |
| 700 | 1 | |a Starr, Shannon |4 aut | |
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10.1007/s00220-006-0135-9 doi (DE-627)OLC2038890617 (DE-He213)s00220-006-0135-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Quantum Spin Systems at Positive Temperature 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S. Starr 2006 Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. Partition Function Coherent State Positive Temperature Gibbs State Quantum Spin System Chayes, Lincoln aut Starr, Shannon aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 269(2006), 3 vom: 15. Nov., Seite 611-657 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:269 year:2006 number:3 day:15 month:11 pages:611-657 https://doi.org/10.1007/s00220-006-0135-9 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_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 269 2006 3 15 11 611-657 |
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10.1007/s00220-006-0135-9 doi (DE-627)OLC2038890617 (DE-He213)s00220-006-0135-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Quantum Spin Systems at Positive Temperature 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S. Starr 2006 Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. Partition Function Coherent State Positive Temperature Gibbs State Quantum Spin System Chayes, Lincoln aut Starr, Shannon aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 269(2006), 3 vom: 15. Nov., Seite 611-657 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:269 year:2006 number:3 day:15 month:11 pages:611-657 https://doi.org/10.1007/s00220-006-0135-9 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_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 269 2006 3 15 11 611-657 |
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10.1007/s00220-006-0135-9 doi (DE-627)OLC2038890617 (DE-He213)s00220-006-0135-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Quantum Spin Systems at Positive Temperature 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S. Starr 2006 Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. Partition Function Coherent State Positive Temperature Gibbs State Quantum Spin System Chayes, Lincoln aut Starr, Shannon aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 269(2006), 3 vom: 15. Nov., Seite 611-657 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:269 year:2006 number:3 day:15 month:11 pages:611-657 https://doi.org/10.1007/s00220-006-0135-9 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_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 269 2006 3 15 11 611-657 |
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10.1007/s00220-006-0135-9 doi (DE-627)OLC2038890617 (DE-He213)s00220-006-0135-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Quantum Spin Systems at Positive Temperature 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S. Starr 2006 Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. Partition Function Coherent State Positive Temperature Gibbs State Quantum Spin System Chayes, Lincoln aut Starr, Shannon aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 269(2006), 3 vom: 15. Nov., Seite 611-657 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:269 year:2006 number:3 day:15 month:11 pages:611-657 https://doi.org/10.1007/s00220-006-0135-9 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_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 269 2006 3 15 11 611-657 |
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10.1007/s00220-006-0135-9 doi (DE-627)OLC2038890617 (DE-He213)s00220-006-0135-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Biskup, Marek verfasserin aut Quantum Spin Systems at Positive Temperature 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © M. Biskup, L. Chayes and S. Starr 2006 Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. Partition Function Coherent State Positive Temperature Gibbs State Quantum Spin System Chayes, Lincoln aut Starr, Shannon aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 269(2006), 3 vom: 15. Nov., Seite 611-657 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:269 year:2006 number:3 day:15 month:11 pages:611-657 https://doi.org/10.1007/s00220-006-0135-9 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_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 269 2006 3 15 11 611-657 |
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Enthalten in Communications in mathematical physics 269(2006), 3 vom: 15. Nov., Seite 611-657 volume:269 year:2006 number:3 day:15 month:11 pages:611-657 |
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Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. © M. Biskup, L. Chayes and S. Starr 2006 |
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Abstract We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins $$\mathcal{S}$$ satisfy $$\beta\ll\sqrt\mathcal{S}$$. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with $$\mathcal{S}\gg1$$. The most notable examples are the quantum orbital-compass model on $$\mathbb{Z}^2$$ and the quantum 120-degree model on $$\mathbb{Z}^3$$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. © M. Biskup, L. Chayes and S. Starr 2006 |
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