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. 

 

 

 

related items

• 5 conformal field theory(CFT)

 

 

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