"Various concepts of limit in statistical physics"의 두 판 사이의 차이
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| 13번째 줄: | 13번째 줄: | ||
** a : lattice spacing | ** a : lattice spacing | ||
** V : volume | ** V : volume | ||
| − | |||
| − | |||
* continuum limit<br> | * continuum limit<br> | ||
** sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant<br> | ** sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant<br> | ||
| + | |||
| + | * scaling limit<br> | ||
| + | ** sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed | ||
| + | |||
* thermodynamic limit<br> | * thermodynamic limit<br> | ||
** a model is taken to the thermodynamic limit by increasing the volume together with the particle number so that the average particle number density remains constant.<br> | ** a model is taken to the thermodynamic limit by increasing the volume together with the particle number so that the average particle number density remains constant.<br> | ||
** http://en.wikipedia.org/wiki/Thermodynamic_limit<br> | ** http://en.wikipedia.org/wiki/Thermodynamic_limit<br> | ||
* infrared limit<br> | * infrared limit<br> | ||
| − | ** sending V to infinity, while keeping a constant<br> | + | ** sending V to infinity, while keeping the lattice spacing a constant<br> |
* ultraviolet limit<br> | * ultraviolet limit<br> | ||
| + | ** ??<br> | ||
| + | |||
| + | * | ||
| 38번째 줄: | 43번째 줄: | ||
<h5>memo</h5> | <h5>memo</h5> | ||
| − | + | * 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 | ||
2010년 8월 19일 (목) 21:54 판
introduction
concept of limit
- notations
- N : number of sites
- a : lattice spacing
- V : volume
- continuum limit
- sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
- sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
- scaling limit
- sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed
- thermodynamic limit
- a model is taken to the thermodynamic limit by increasing the volume together with the particle number so that the average particle number density remains constant.
- http://en.wikipedia.org/wiki/Thermodynamic_limit
- a model is taken to the thermodynamic limit by increasing the volume together with the particle number so that the average particle number density remains constant.
- infrared limit
- sending V to infinity, while keeping the lattice spacing a constant
- 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
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