"Various concepts of limit in statistical physics"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “* Princeton companion to mathematics(Companion_to_Mathematics.pdf)” 문자열을 “” 문자열로) |
Pythagoras0 (토론 | 기여) |
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==introduction== | ==introduction== | ||
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| − | ==concept | + | ==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=== | ||
| + | * ?? | ||
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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. | 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. | ||
| 39번째 줄: | 35번째 줄: | ||
http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf | http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf | ||
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==memo== | ==memo== | ||
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* 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 | * 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 | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q1103484 Q1103484] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'thermodynamic'}, {'LEMMA': 'limit'}] | ||
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'}]