Critical phenomena
http://bomber0.myid.net/ (토론)님의 2011년 10월 1일 (토) 07:32 판
introduction
- In this sense, the thermodynamic functions seem to display scale invariance around the critical point (for systems that have a critical point!), with the scaling variable t=(1-T/Tc).
- Note that the logarithm y=log x obeys y(ax)=y(x) + log a.
- It is scale invariant with exponent 0 (and a scale-dependent shift.)
- This is related to the famous formula
\(\lim_{p\to 0}\frac{x^p-1}{p} = \log x\)
which shows that logs are a special case of power law functions with power 0. - basics of magnetism
examples
- liquid-vapour critical point
- paramagnetic-ferromagnetic transition
- multicomponent fluids
- alloys
- superfulids
- superconductors
- polymers
- fully developed turbulence
- quark-gluon plasma
- early universe
E.A. Guggenheim, The Journal of Chemical Physics 13, 253-261 (1945).
Tromp, R. M., W. Theis, and N. C. Bartelt. 1996. Real-Time Microscopy of Two-Dimensional Critical Fluctuations: Disordering of the Si(113)-( 3 x 1) Reconstruction. Physical Review Letters 77, no. 12: 2522. doi:10.1103/PhysRevLett.77.2522.
history
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
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