"Critical phenomena"의 두 판 사이의 차이
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<h5>introduction</h5> | <h5>introduction</h5> | ||
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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. | ||
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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). | ||
| − | R. M. | + | 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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2011년 1월 26일 (수) 16:31 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.
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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