Advanced Statistical Mechanics / Statistical Mechanics I (2026)

Syllabus

Nature realizes a rich variety of phases of matter and phase transitions. Remarkably, certain phase transitions exhibit critical phenomena that are insensitive to microscopic details and depend solely on universal characteristics such as symmetry. In this course, we develop the fundamental theoretical framework for describing phase transitions and critical phenomena, with particular emphasis on the renormalization group and the concept of universality, which underlie the modern theoretical physics. From a technical perspective, we learn basic methods of statistical field theory.

Teaching Assistant: Haruki Shimizu

Contents

  1. [Apr. 6th] Introduction and overview
  2. [Apr. 13th] No lecture (due to the university schedule)
  3. [Apr. 20th] Path integral (Landau-Ginzburg theory), Symmetry
    [Locality in Landau-Ginzburg theory (pdf)]
  4. [Apr. 27th] Gaussian theory (1) (partition function)
  5. [May 4th] No lecture (due to the national holiday)
  6. [May 7th (Thursday)] Gaussian theory (2) (correlation functions)
  7. [May 11th] No lecture (due to the university schedule)
  8. [May 18th] Renormalization group (video)
  9. [May 25th] No lecture (due to my attendance at a workshop)
  10. [Jun. 1st] No lecture (due to the university schedule)
  11. [Jun. 2nd (Tuesday)] Scaling, Dimensional analysis
  12. [Jun. 8th] Gaussian fixed point, Emergent symmetry
  13. [Jun. 15th] Perturbative renormalization group
  14. [Jun. 22nd] Operator product expansion
  15. [Jun. 29th] Wilson-Fisher fixed point, Logarithmic corrections in four dimensions, Asymptotic expansion (pdf)
  16. [Jul. 6th] O(N) model, Epsilon expansion, Nambu-Goldstone modes
  17. [Jul. 13th] Hohenberg-Mermin-Wagner theorem
  18. [Jul. 20th] No lecture (due to the national holiday)
  19. [Jul. 27th] Berezinskii-Kosterlitz-Thouless transition

Reports

References

[Textbooks]

[Others]