Vague Quantum Criticality

Rossen Roussev

1. I will remind the audience what classical criticality is - order parameters, their symmetry, power law behaviors of physical quantities and above all the role of the interplay between interactions and fluctuations for critical phenomena. I will outline the idea and the procedure of the Renormalization Group transformation.
2. I will then talk about q u a n t u m critical phenomena - where they come from, about the differences and the similarities with the classical case, new critical exponents, and will give several simple examples of specific physical systems where a quantum critical model is essential.

My plan is to emphasize on the physics, at least the way I see it, and neglect the sometimes complicated mathematical technicalities. I will rely on the audience to stop me at any time so we can mutually reach a satisfactory physical understanding of some of the most important lingo in this business: path integrals, critical exponents, fixed points and the like. As a side effect, I hope to relate the reasons why I find this field challenging and exciting.

References:

Classical critical phenomena:
1) S. K. Ma, Modern Theory of Critical Phenomena, Benjamin, Readin 1976
2) N. Goldenfeld, Lectures on Phase Transitions and the Renormalization
   Group, Addison-Wesley, Reading 1992
3) M. E. Fisher, The Renormalization Group in the Theory of Critical
   Behavior, Rev. Mod. Phys., 46, 597 (1974)
4) C. Domb and M. S. Green, Phase Transition and Critical Phenomena v.6,
   Academic Press, London 1976. Especially articles
   Field Theoretical Approach to Critical Phenomena, E. Brezin, J. C. Le
   Guillou and J. Zinn-Justin
   The 1/n Expansion, Shang-Keng Ma
   but the entire volume is very useful indeed.

Quantum critical phenomena:
Seminal papers:
1) J. A. Hertz, Phys. Rev. B 14, 1165 (1976)
2) A. J. Millis, Phys. Rev. B 48, 7183 (1993)
Reviews:
3) Thomas Vojta, Quantum Phase Transitions in Electronic Systems,
   cond-mat//9910514
4) T. R. Kirkpatrick and D. Belitz, Quantum Phase Transitions in Electronic
   Systems, cond-mat//9707001
Books:
5) S. Sachdev, Quantum Phase Transitions, Cambridge University Press,
   Cambridge 1999