Lecture Notes of Statistical Mechanics

Lecture notes of the Master's degree course "Statistical Mechanics" of Prof. Enzo Orlandini at the University of Padova. The notes are updated for the "Physics of Data" master course a.y. 2023/2024.

Author: Alice Pagano (University of Padova)

Contributors:

• Jacopo Carotenuto (2023/2024)
• Carlo Sgorlon Gaiatto and Noemi Manara (2022/2023)

Table of Contents

1. Recall of Thermodynamics
2. Equilibrium phases and thermodynamics of phase transitions
3. Recall of statistical mechanics and theory of ensembles
4. Statistical mechanics and phase transitions
5. Role of the models in statistical mechanics
6. Some exactly solvable models of phase transitions
7. The role of dimension, symmetry and range of interactions in phase transitions
8. Mean field theories of phase transitions and variational mean field
9. Non ideal fluids: Mean field theory, Van der Walls, Virial expansion and Cluster expansion
10. Landau theory of phase transition for homogeneous systems
11. Role of fluctuations in critical phenomena: Ginzburg criterium, Coarse-graining and Ginzburg-Landau theory of phase transitions
12. Widom’s scaling theory. Block-spin Kadanoff’s transformation
13. Renormalization group theory. Universality
14. Spontaneous symmetry breaking

Folder Organization

The code of the notes is organized in multiple directories as:

• Bibliography: in this directory I stored the .tex subfile for the bibliography.
• Frontpage: .tex subfile for the frontpage of the notes.
• Arguments: each arguments has it's own chapter and .tex subfile.
• Utility: contains .tex files for packages, settings and new commands.
• Main: .tex file for the full document.