Ph 127b – Winter 2007

                  Statistical Physics of interacting systems - critical phenomena

 

 

 

Instructor:  

            Gil Refael
            117 Sloan Annex, x4705

            refael{at}caltech.edu
            Office Hours : Friday 3-4pm.

 

Grader:

            Waheb Bishara

            131 Sloan Annex, x2288

            waheb{at}caltech.edu
            Office Hours : Monday 5-6:30pm.

 

Syllabus and General Info

 

Special announcements:
   

FINAL EXAM

Please read the instructions in the cover page first : Final Exam Cover Page
The exam is due on Friday, March 21st , 5pm, in Gil's mailbox. Good Luck!     Final Exam

Lecture Notes

            Week 1  Continuous phase transition, symmetry breaking, correlation length.
            Week 2  Long range vs. quasi long range order, Mermin-Wagner theorem, exact solution of the Ising model, transfer matrices. 
                            chapters 2.8, 3.1, 3.2 in Goldenfeld. 
            Week 3  Correlation function using transfer matrices. Mean-field theory of the Ising model. Landau mean field theory. 
                            chapters  3.3-3.7, and 5.1-5.4 in Goldenfeld.
             Week 4  Examples of Landau theory of phase transitions

                           Renormalization Group - 1D Ising

                           Renormaliation Group - General Case (not covered in class).

             Week 5  Inhomogeneous systems, Landau free energy functional, path integrals, saddle point approximation,etc.

             Week 6  Ginzburg criterion for failure of Landau mean field theory. Scaling hypothesis.

             Week 7  Notes on domain walls and the lower critical dimension

                           Naive renormalization of the Ising free energy: Scaling without decimation

                           After clearing up the domain wall issues, we will go back to scaling which is in the end of week 6 notes.

                            Relevant book chapters: Chapters 8.1, 8.2 (Scaling). Also see: Chapter 9 - Renormalization group. 

            Week 8  Epsilon expansion and the Wilson-Fisher fixed point. Chapter 9 and chapter 12. 

Homework

 

           Problem Set 1 Solutions

           Problem Set 2 Solutions

           Problem Set 3 Solutions

 

 Supplements