"Critical phenomena"의 두 판 사이의 차이
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<h5>introduction</h5> | <h5>introduction</h5> | ||
| − | * 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).''' | + | * 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).''' |
| − | * This is related to the famous formula<br> | + | * 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<br><math>\lim_{p\to 0}\frac{x^p-1}{p} = \log x</math><br> which shows that logs are a special case of power law functions with power 0.<br> | ||
* [[basics of magnetism]] | * [[basics of magnetism]] | ||
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.
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