Physics 127b – Stat. Mech. of Critical Phenomena

·       Instructor:

Gil Refael

Office: 117 Sloan annex

Email: refael@caltech.edu

Ext.: 4705

·       Teaching assistant:

Waheb Bishara

Office: 131 Sloan Annex

Email: waheb@caltech.edu

·       Syllabus (and tentative program):

Week 1 - Critical phenomena, broken symmetries, and scaling  - general introduction.  

Week 2 - 1D Ising model: exact solution, transfer matrices, correlation length.

Week 3 - Mean field theory.

Week 4 - Landau theory of phase transitions.

Week 5 - Non-uniform Landau theory, path integral approach, Hubbard-Stratonovich transformation.

Week 6 - Fluctuations, correlations, Mermin-Wagner theorem.

Week 7 - Scaling, renormalization group (RG) approach: real-space RG, percolation.

Week 8 - Epsilon expansions, Wilson-Fisher fixed point.  

Week 9 - X-Y model, Kosterlitz-Thouless transition.

Week 10 - Dynamics: fluctuation dissipation theorem (if time allows).

·       Books:

Main textbook:

“Lectures on Phase Transitions and the Renormalization Group”, Goldenfeld.  

Other recommended books:

“Scaling and Renormalization in Statistical Physics”, Cardy.

“Statistical Physics”, Landau and Lifshitz.

“Introduction to RG Methods in Physics”, Crezwick, Farach, Poole.

“Modern Theory of Critical Phenomena”, S. K. Ma.