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Course Announcements:
- 6/18: all solutions are posted and grades have been sent to the registrar. Thanks for a great quarter!
Course Information:
Instructor: Sid Parameswaran, Assistant Professor
310J Rowland Hall, sidp_at_uci.edu
Office Hours: Mondays 3:00-4:00PM.
Lectures: Monday/Wednesday 12:30PM - 1:50PM, 1427 Donald Bren Hall.
Final Exam: No in-class final; term papers due June 8.
Overview:
This is the second in a three-course graduate-level sequence on statistical mechanics. Roughly, this quarter we will study the collective behavior of systems of many interacting particles, leading us naturally to the topics of phase transitions, critical phenomena, and universality, which we will explore using the ideas of statistical field theory and the renormalization group. Advanced topics that I might discuss, given time, include the Berezinskii-Kosterlitz-Thouless phase transition and the basic notions of conformal field theory.
Prerequisites:
As this is the second course in the sequence, you are expected to be familiar with quantum and statistical mechanics and electrodynamics at the level of PHY214A. If you have not taken this course, but still would like to attend the lectures or sign up for the class, please contact me beforehand. As in all courses and particularly advanced ones, you will get as much out of this class as you put in to it - so keep up with the homework and readings!
Textbook(s):
I plan to make my lecture notes available online through the quarter; these will borrow from various sources. There are several textbooks and monographs that cover the topics of this course.
As a basic text, I plan to use Mehran Kardar's Statistical Physics of Fields. Other useful books include:
- Scaling and Renormalization in Statistical Physics, John Cardy, Cambridge University Press. An excellent, if terse, overview of the subject. Makes extensive use of operator product expansions (OPEs), which can be somewhat subtle. Includes a beautiful discussion of conformal field theory.
- Lectures on Phase Transitions and the Renormalization Group, Nigel Goldenfeld, Frontiers in Physics Series (Vol. 85), Westview Press. Classic text on the subject and especially useful in understanding the RG.
- Principles of Condensed Matter Physics, P.M. Chaikin & T.C. Lubensky, Cambridge University Press. The unofficial Bible of "soft matter" physics, an often indispensable guide to topics such as liquid crystals, hydrodynamics, and response.
Lecture Notes and Course Outline:
As mentioned above, I will post my handwritten notes whenever possible and appropriate, but I suggest that you take notes in class - particularly as this is a graduate course, I hope there will be a fair amount of discussion in 'real time' that you might like to have a record of.
The notes are organized into files by topic, but the lectures sometimes span multiple files/are contained within a single file. I'll post a complete set as a separate link at the end of the quarter.
1. C0llective Phenomena: Particles to Fields
2. Statistical fields, saddle points, and symmetry breaking
3. Fluctuations about saddle points; upper/lower critical dimension; Ginzburg criterion
5. Renormalization Group I: Foundations
7. Perturbing the Gaussian model: Preliminaries
8. Renormalization Group II: Perturbative RG & ϵ-Expansion
10. The d=2 XY Model: Topological defects, Coulomb gas and the KT transition
If you prefer a single large file with all the lectures, here is the combined PDF (warning, 109 pages, file size~35MB).
Here is a rough schedule of topics to be covered. Some topics may bleed into subsequent lectures.
Warning: this is subject to change without notice as the class progresses.
March 28: Collective behavior: microscopic vs. phenomenological approaches.
March 30:Phase transitions, critical behavior, critical exponents, universality.
April 4: Statistical field theories, saddle points;
April 6: no class/substitute lecture Thursday, April 7. Symmetry breaking, Goldstone modes, domain walls.
April 11: Fluctuations, correlations.
April 13: Susceptibilities.
April 18: Fluctuation corrections to saddle-points; Ginzburg Criterion.
April 20: no class/substitute lecture Thursday April 21. scaling. self-similarity, conceptual foundations of RG.
April 25: RG framework
April 27: RG framework; exponents in terms of scaling dimensions
May 2: Gaussian model
May 4: Perturbing the Gaussian model
May 9: Perturbative RG : first order
May 11: Perturbative RG; second order
May 16: ϵ-expansion, Wilson-Fisher fixed point
May 18: Nonlinear sigma models: RG.
May 23: XY model, topological defects, Coulomb gas.
May 25: RG for the Coulomb gas; start Kosterlitz-Thouless.
May 30: Memorial Day, no class
June 1: Finish Kosterlitz-Thouless; Course overview. All incomplete problem sets due.
June 8: final projects due via email only.
I may have to miss 1-2 lectures during the quarter, owing to seminar/conference commitments; I hope to make these up during the quarter and will poll the class on a suitable date(s) for the make-up lecture(s).
Notes will be posted as they become available.
Problem Sets:
There will be 4-5 problem sets posted intermittently through the quarter, and they will be due 7-10 days after posting. I am reasonably flexible about deadlines, but owing to the need to assign a grade, all the sets will need to be completed eventually.
Problem Set 1, due by 4pm Thursday, April 14.
Problem Set 2, due by 4pm Thursday, April 21.
Problem Set 3, due by 4pm Thursday, May 5.
Problem Set 4, due by 4pm Tuesday, May 25.
Solutions in PDF form available on request - please email me directly if you require these.
Grading:
Your grade will be based on the problem sets (60%), a final term paper (30%), and class participation (10%).
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