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.

- Fluctuations, continuous transitions and critical phenomena
- Crackling noise and depinning transitions
- The idea behind the renormalization group
- Phase diagrams, fixed points, & scaling
- Bifurcation theory, & normal forms, and logarithms
- ε-expansions
- Kosterlitz-Thouless and the lower critical dimension
- Disordered systems and glasses
- Conformal bootstrap methods
- 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
- References for journal clubs
- Topics for special projects
- Introductory lectures
- Intro renormalization-to-scaling writeup

Last Modified: July 28, 2017

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