"Various concepts of limit in statistical physics"의 두 판 사이의 차이
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| (사용자 3명의 중간 판 21개는 보이지 않습니다) | |||
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| − | + | ==introduction== | |
| − | + | ||
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| − | + | ==concept of limit== | |
| − | + | ===notations=== | |
| + | * N : number of sites | ||
| + | * a : lattice spacing | ||
| + | * V : volume | ||
| + | ===continuum limit=== | ||
| + | * used in the lattice model | ||
| + | * sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant | ||
| + | * applied to spin chains whose continuum limit yields conformal field theories | ||
| + | === scaling limit=== | ||
| + | * sounds similar to continuum limit | ||
| + | * sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed | ||
| + | ===thermodynamic limit=== | ||
| + | * increasing the volume together with the particle number so that the average particle number density remains constant. | ||
| + | * http://en.wikipedia.org/wiki/Thermodynamic_limit | ||
| + | ===infrared limit=== | ||
| + | * sending V to infinity, while keeping the lattice spacing a constant | ||
| + | ===ultraviolet limit=== | ||
| + | * ?? | ||
| + | |||
| − | + | ||
| − | + | The c-theorem implies that the infra-red limit, where the scale goes to innity, and the ultra-violet limit, where the scale vanishes, are fixed points of the renormalisation group. | |
| − | + | http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf | |
| − | + | ||
| − | + | ||
| − | + | ==memo== | |
| − | |||
| − | |||
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| − | + | * Glimm, J., Jaffe, A.: [http://www.springerlink.com/content/t413601r24427883/ Particles and scaling for lattice fields and Ising models]. Commun. Math. Phys.51, 1 (1976) | |
| + | * Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys.74, 119 (1980) | ||
| + | * Fröhlich, J., Spencer, T.: Some recent rigorous results in the theory of phase transitions and critical phenomena. Séminaire Bourbaki No. 586 (February 1982) | ||
| + | * Sinai, Ya.G.: Mathematical foundations of the renormalization group method in statistical physics. In: Mathematical problems in theoretical physics. Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds.). Lectures Notes in Physics, Vol. 80. Berlin, Heidelberg, New York: Springer 1978 | ||
| − | + | [[분류:개인노트]] | |
| + | [[분류:physics]] | ||
| + | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
| − | + | ==메타데이터== | |
| − | + | ===위키데이터=== | |
| − | + | * ID : [https://www.wikidata.org/wiki/Q1103484 Q1103484] | |
| − | + | ===Spacy 패턴 목록=== | |
| − | + | * [{'LOWER': 'thermodynamic'}, {'LEMMA': 'limit'}] | |
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2021년 2월 17일 (수) 02:31 기준 최신판
introduction
concept of limit
notations
- N : number of sites
- a : lattice spacing
- V : volume
continuum limit
- used in the lattice model
- sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
- applied to spin chains whose continuum limit yields conformal field theories
scaling limit
- sounds similar to continuum limit
- sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed
thermodynamic limit
- increasing the volume together with the particle number so that the average particle number density remains constant.
- http://en.wikipedia.org/wiki/Thermodynamic_limit
infrared limit
- sending V to infinity, while keeping the lattice spacing a constant
ultraviolet limit
- ??
The c-theorem implies that the infra-red limit, where the scale goes to innity, and the ultra-violet limit, where the scale vanishes, are fixed points of the renormalisation group.
http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf
memo
- Glimm, J., Jaffe, A.: Particles and scaling for lattice fields and Ising models. Commun. Math. Phys.51, 1 (1976)
- Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys.74, 119 (1980)
- Fröhlich, J., Spencer, T.: Some recent rigorous results in the theory of phase transitions and critical phenomena. Séminaire Bourbaki No. 586 (February 1982)
- Sinai, Ya.G.: Mathematical foundations of the renormalization group method in statistical physics. In: Mathematical problems in theoretical physics. Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds.). Lectures Notes in Physics, Vol. 80. Berlin, Heidelberg, New York: Springer 1978
메타데이터
위키데이터
- ID : Q1103484
Spacy 패턴 목록
- [{'LOWER': 'thermodynamic'}, {'LEMMA': 'limit'}]