Various concepts of limit in statistical physics
imported>Pythagoras0님의 2012년 10월 28일 (일) 17:04 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
- 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
history
encyclopedia==
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles==
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links
- N : number of sites
- a : lattice spacing
- V : volume
- 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
- sounds similar to continuum limit
- sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed
- increasing the volume together with the particle number so that the average particle number density remains constant.
- http://en.wikipedia.org/wiki/Thermodynamic_limit
- sending V to infinity, while keeping the lattice spacing a constant
- ??
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=