Overview of the course

Fig. 1 Outline of the course.

The road map of the course is shown in the figure Outline of the course.

The statistical mechanics (II) goes beyond the statistical mechanics (I) in a sense that we are going to discuss the physics of interacting systems.

One of the conceptual important breakthrough in statistical mechanics is the renormalization group theory. That will be the first theme of our semester. The idea of renormalization group is so important that you will see it in various different branches of physics. e.g. Condensed matter physics, field theories, atomic physics, etc. The idea of renormalization group on the one hand answers the origin of anomalous dimension, on the other hand, it completes the concept of effective theory and forming a framework for a phenomenological theory.

To build our understanding of the renormalization group theory, we will start from the review of mean-field theory and introduce the Landau theory for phases and phase transitions. We will discuss the postulates of these theories, the limitations and attempts to fix/improve the theory. After that, we will introduce the renormalization group theory and use it to study the critical phenomena of the Ising models.

After we are equipped with the concept of renormalization group, we will revisit the Ising model again and introduce other approaches for the interacting system such as series expansion, duality and exact solutions. With these tools, we have a better feeling about how to deal with the interacting systems.

Then, we will discuss the \(XY\) model, interacting bosons and interacting fermions depends on the progress and the learning status of the class.