Statistical Physics 7653, Fall 2018

Systems that are undergoing a qualitative change of behavior often look the same on different scales -- they exhibit an emergent scale invariance. Renormalization-group methods discovered largely at Cornell for thermodynamic critical points are now being used to explain emergent scale invariance for the onset of chaos, percolation of oil-bearing porous rock, earthquakes and avalanches at depinning transitions, quantum fluctuations, correlated metals and Fermi liquids, the motion of interfaces, and the flocking of birds, wildebeests, and bacteria. Conversely, new ideas from string theory and mathematics have led to a deeper understanding of critical phenomena.

The course is designed for graduate students in physics who have taken a semester of graduate-level statistical mechanics.

Possible topics

1. Fluctuations, continuous transitions and critical phenomena
2. Crackling noise and depinning transitions
3. The idea behind the renormalization group
4. Phase diagrams, fixed points, & scaling
5. Bifurcation theory, & normal forms, and logarithms
6. ε-expansions
7. Kosterlitz-Thouless and the lower critical dimension
8. Disordered systems and glasses
9. Conformal bootstrap methods
10. Quantum critical points
11. Fermi liquid theory and the renormalization group

Required texts

• John Cardy, "Scaling and Renormalization in Statistical Physics", Cambridge University Press, 1996.
• "Statistical Mechanics: Entropy, Order Parameters, and Complexity", Sethna, Oxford (original edition 2006, second edition in preparation). (Second edition draft online at https://sethna.lassp.cornell.edu/StatMech/.)

• Homework exercises
• References for journal clubs
• Topics for special projects
• Introductory lectures
• Intro renormalization-to-scaling writeup

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).