A225
Course Coordinator: 
Reiko Toriumi
Statistical Mechanics, Critical Phenomena and Renormalization Group
Description: 

The course is designed as an introduction to the methods of statistical mechanics and evolves into critical phenomena and the renormalization group.
The analogy between statistical field theory and quantum field theory may be addressed throughout the course.
Key concept which will be emphasized in this course is universality; we concern systems with a large number of degrees of freedom which may interact with each other in a complicated and possibly highly non-linear manner, according to laws which we may not understand. However, we may be able to make progress in understanding behavior of such problems by identifying a few relevant variables at particular scales. The renormalization group addresses such a mechanism.
Some selected topics are planned to be covered, such as conformal field theory, vector models/matrix models, SLE.

Aim: 
Students will obtain understanding of modern concepts and techniques in statistical mechanics/statistical field theory, geared toward the common concepts appearing in quantum field theory, namely critical phenomena and the renormalization group. The course is mainly targeted at students who are interested in theoretical works. The course is planned to develop to some advanced topics in the later half.
Course Content: 

We plan to cover the following material from Pathria and Beale:
- Chap 1: The Statistical Basis of Thermodynamics
- Chap 2: Elements of Ensemble Theory
- Chap 3: The Canonical Ensemble
- Chap 4: The Grand Canonical Ensemble
- Chap 5: Formulation of Quantum Statistics
- Chap 6: The Theory of Simple Gases
- Chap 7: Ideal Bose Systems
- Chap 8: Ideal Fermi Systems
- Chap 9: Statistical Mechanics of Interacting Systems: Cluster Expansions Method

From Cardy,
Chapter 3: The renormalization group idea
Chapter 5: The perturbative renormalization group
Chapter 11: Conformal symmetry

We may cover some more selected topics such as conformal field theory, vector models/matrix models, SLE, if the time allows.

The instructor reserves the right to make minor changes in the syllabus, as needed.

Note: homework asignments are due every Wednesday, before the class. There will be no late homework submission accepted, unless it is discussed with the instructor beforehand.

Lecture meets with Toriumi: Wed:10-12 Fri: 10-11
Discussion meets with Toriumi: Mon: 10-11

The exams will be closed book, but you can bring a single sheet of paper on which you can
write what you want to refer to during the exam on both sides.  Note that I will decide how many midterms we will do shortly after we start the course. Depending on the number of midterms, there will be adjustments on the distribution for the weights of each element (i.e., homework and exams).

Expectations: Students are expected to attend every lecture and discussion. Students are responsible for the materials that are covered in lectures. Note that in lectures, we will cover additional materials that are not discussed in the textbooks. Discussion sessions are designed for you to practice solving problems.
One of the important things in your scientific career is good communication. You will have collaborators, peers, students and public for you to communicate your scientific results with. Without you communicating well about your results, your results may well be equal to nothing. Students are therefore expected to practice good communication with the instructor. Your homework, and your exams for example, are ways to communicate with the instructor. Keep in mind that it is not just about showing that you solved the problems, but it is about showing and demonstrating that your work is legitimate. You are expected to work toward this goal.

Course Type: 
Elective
Credits: 
2
Assessment: 
Weekly assignments (40%); midterm exam (30%); final exam or project (30%)
Text Book: 
Pathria and Beale, Statistical Mechanics, 2011 Elsevier
John Cardy, Scaling and Renormalization in Statistical Physics
Reference Book: 
John Cardy, Conformal Field Theory and Statistical Mechanics
David Tong, online lectures on Statistical Field Theory
John Cardy, Conformal Invariance and Statistical Mechanics (lecture notes)
Prior Knowledge: 

Students should have knowledge of Classical Mechanics and Quantum Mechanics to advanced undergraduate level.