"Critical phenomena"의 두 판 사이의 차이
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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).''' |
* 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.) | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
2020년 11월 13일 (금) 02:50 판
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).
- 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