"Critical phenomena"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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==introduction== | ==introduction== | ||
| − | * '''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).''' | + | * 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. | * 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.) | * It is scale invariant with exponent 0 (and a scale-dependent shift.) | ||
| 38번째 줄: | 38번째 줄: | ||
| + | ==history== | ||
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| + | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| + | ==related items== | ||
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| + | * [[5 conformal field theory(CFT)]] | ||
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| + | ==encyclopedia== | ||
| + | |||
| + | * http://en.wikipedia.org/wiki/ | ||
| + | * http://www.scholarpedia.org/ | ||
| + | * [http://eom.springer.de/ http://eom.springer.de] | ||
| + | * http://www.proofwiki.org/wiki/ | ||
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| + | ==books== | ||
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| + | * [[2011년 books and articles]] | ||
| + | * http://library.nu/search?q= | ||
| + | * http://library.nu/search?q= | ||
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| 47번째 줄: | 84번째 줄: | ||
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| + | ==articles== | ||
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| + | * 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/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html] | ||
| + | * http://dx.doi.org/ | ||
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| + | ==question and answers(Math Overflow)== | ||
| + | |||
| + | * http://mathoverflow.net/search?q= | ||
| + | * http://mathoverflow.net/search?q= | ||
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| + | ==blogs== | ||
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| + | * 구글 블로그 검색<br> | ||
| + | ** http://blogsearch.google.com/blogsearch?q=<br> | ||
| + | ** http://blogsearch.google.com/blogsearch?q= | ||
| + | * http://ncatlab.org/nlab/show/HomePage | ||
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| + | ==experts on the field== | ||
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| + | * http://arxiv.org/ | ||
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| + | ==links== | ||
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| + | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
| + | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
| + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | ||
| + | * http://functions.wolfram.com/ | ||
[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
| + | [[분류:migrate]] | ||
2020년 11월 13일 (금) 02:50 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/
books
expositions
- Scaling, universality, and renormalization: Three pillars of modern critical phenomena ftp://162.105.205.230/pub/Books/%CE%EF%C0%ED/%CE%EF%C0%ED%D1%A7%CA%B7/History_of_Modern_Physics/Statistical%20Physics%20and%20Fluids/Scaling,%20universality,%20and%20renormalization.pdf
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