"Critical phenomena"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<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).''' 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> limp-->0 (x^p-1)/p = log x<br> which shows that logs are a special case of power law functions with power 0. | + | * 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<br> limp-->0 (x^p-1)/p = log x<br> which shows that logs are a special case of power law functions with power 0. | ||
| + | * [[basics of magnetism]] | ||
| − | + | ||
| 9번째 줄: | 11번째 줄: | ||
<h5>examples</h5> | <h5>examples</h5> | ||
| − | liquid-vapour critical point | + | * liquid-vapour critical point |
| − | + | * paramagnetic-ferromagnetic transition | |
| − | paramagnetic-ferromagnetic transition | + | * multicomponent fluids |
| − | + | * alloys | |
| − | multicomponent fluids | + | * superfulids |
| − | + | * superconductors | |
| − | alloys | + | * polymers |
| − | + | * fully developed turbulence | |
| − | superfulids | + | * quark-gluon plasma |
| − | + | * early universe | |
| − | superconductors | ||
| − | |||
| − | polymers | ||
| − | |||
| − | fully developed turbulence | ||
| − | |||
| − | quark-gluon plasma | ||
| − | |||
| − | early universe | ||
2011년 10월 1일 (토) 07:25 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
limp-->0 (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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