Ideas and methods developed in studying continuous phase transitions have become widely applied throughout physics. Renormalization-group methods are used not only for thermodynamic critical points, but for studying 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 and wildebeests. Conversely, new ideas from string theory and mathematics have led to a deeper understanding of critical phenomena in two dimensions. Statistical physics this semester will attempt to provide an introduction into a selection of these subjects.

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

- Fluctuations, continuous transitions and critical phenomena
- Mean-field theory, bifurcations, & normal forms
- The idea behind the renormalization group
- Phase diagrams, fixed points, & scaling
- ε-expansions
- Kosterlitz-Thouless and the lower critical dimension
- Crackling noise and depinning transitions
- Disordered systems and glasses
- Conformal invariance and SLE
- Quantum critical points
- Fermi liquid theory and the renormalization group

- John Cardy, "Scaling and Renormalization in Statistical Physics", Cambridge University Press, 1996.
- "Statistical Mechanics: Entropy, Order Parameters, and Complexity", Sethna, Oxford (2006). (Online at http://pages.physics.cornell.edu/sethna/StatMech/.)

- Homework exercises
- Other texts and references
- Topics for special projects
- Introductory lectures
- Intro renormalization-to-scaling writeup

Last Modified: August 18, 2015

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