"Various concepts of limit in statistical physics"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
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| − | ==concept | + | ==concept of limit== |
===notations=== | ===notations=== | ||
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===ultraviolet limit=== | ===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. | ||
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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== | ||
2020년 12월 28일 (월) 05:20 판
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