Various concepts of limit in statistical physics
http://bomber0.myid.net/ (토론)님의 2010년 8월 19일 (목) 21:32 판
introduction
concept of limit
- notations
- N : number of sites
- a : lattice spacing
- V : volume
- scaling limit
- sending the lattice spacing a to zero, , while keeping the volume V=Na constant
- 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
- 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 a constant
- sending V to infinity, while keeping 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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