Critical phenomena

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. 

 

 

 

history

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• 5 conformal field theory(CFT)