"Various concepts of limit in statistical physics"의 두 판 사이의 차이
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| 14번째 줄: | 14번째 줄: | ||
* V : volume | * V : volume | ||
===continuum limit=== | ===continuum limit=== | ||
| − | * used in the lattice model | + | * 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 | + | * 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 | * applied to spin chains whose continuum limit yields conformal field theories | ||
=== scaling limit=== | === scaling limit=== | ||
| 21번째 줄: | 21번째 줄: | ||
* sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed | * sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed | ||
===thermodynamic limit=== | ===thermodynamic limit=== | ||
| − | * increasing the volume together with the particle number so that the average particle number density remains constant. | + | * increasing the volume together with the particle number so that the average particle number density remains constant. |
| − | * http://en.wikipedia.org/wiki/Thermodynamic_limit | + | * http://en.wikipedia.org/wiki/Thermodynamic_limit |
===infrared limit=== | ===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=== | ===ultraviolet limit=== | ||
| − | * ?? | + | * ?? |
2020년 11월 16일 (월) 07:47 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