Statistical Mechanics, Critical Phenomena and Renormalization Group

Course 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 Description

An introduction to the methods of statistical mechanics that evolves into critical phenomena and the renormalization group.
The analogy between statistical field theory and quantum field theory is addressed throughout the course.
The key concept emphasized in this course is universality; we are concerned with 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 the behavior of such problems by identifying a few relevant variables at particular scales. The renormalization group addresses such a mechanism.
Some selected topics are covered, such as conformal field theory, vector models/matrix models, and SLE.

Course Contents

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.


Weekly assignments (40%); midterm exam (30%); final exam or project (30%)

Prerequisites or Prior Knowledge

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


Pathria and Beale, Statistical Mechanics, 2011 Elsevier
John Cardy, Scaling and Renormalization in Statistical Physics
Adrian Tanasa's Combinatorial Physics 2021 Oxford.

Reference Books

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)

Research Specialties