Bachelor's Course Advanced Statistical Physics
This course explores the principles and applications of thermodynamics and statistical physics, emphasizing the description of classical many-body systems and touching upon a few simple quantum gasses. We cover the following topics: phase transitions (gas-liquid condensation, magnetic ordering, crystallization, phase separation, and liquid-crystalline order), critical phenomena (exponents, divergent length scales, and fluctuations), and the structure and thermodynamic properties of non-ideal gasses, classical fluids, and liquid crystals. The theoretical framework comprises mean-field theory, a simple renormalization group of spin systems, Landau theory for first- and second-order phase transitions, nucleation theory, the virial expansion for non-ideal atomic gasses, and Onsager theory for anisotropic particles. In addition, the formal relationship of the various thermodynamic potentials (energy, free energy, enthalpy, Gibbs free energy, and grand potential) are related to each other via Legendre transformations; universal thermodynamic identities are also derived.
The notes were originally put together by R. van Roij and later extended and reworked by L. Filion. I subsequently modified these to account for changes in the content and structure of the course. This includes the repartitioning of material between academic years 2021-22 and 2022-23 to accommodate the topic of ideal quantum gases. If you are interested in self-studying the material, I have provided the course schedule of 2024.
