"Critical phenomena"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→메타데이터: 새 문단) |
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==introduction== | ==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. | * 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.) |
* This is related to the famous formula<math>\lim_{p\to 0}\frac{x^p-1}{p} = \log x</math> which shows that logs are a special case of power law functions with power 0. | * This is related to the famous formula<math>\lim_{p\to 0}\frac{x^p-1}{p} = \log x</math> which shows that logs are a special case of power law functions with power 0. | ||
* [[basics of magnetism]] | * [[basics of magnetism]] | ||
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==examples== | ==examples== | ||
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* early universe | * early universe | ||
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E.A. Guggenheim, The Journal of Chemical Physics 13, 253-261 (1945). | 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:[http://dx.doi.org/10.1103/PhysRevLett.77.2522 10.1103/PhysRevLett.77.2522]. | + | 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:[http://dx.doi.org/10.1103/PhysRevLett.77.2522 10.1103/PhysRevLett.77.2522]. |
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==related items== | ==related items== | ||
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* [[5 conformal field theory(CFT)]] | * [[5 conformal field theory(CFT)]] | ||
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==expositions== | ==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 | * 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 | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
2020년 12월 28일 (월) 04:09 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.
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
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