Advanced Statistical Mechanics / Statistical Mechanics I (2026)
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
[Apr. 6th] Introduction and overview
[Apr. 13th] No lecture (due to the university schedule )
[Apr. 20th] Path integral (Landau-Ginzburg theory), Symmetry
[Apr. 27th] Gaussian theory (1) (partition function)
[May 4th] No lecture (due to the national holiday)
[May 7th (Thursday)] Gaussian theory (2) (correlation functions)
[May 11th] No lecture (due to the university schedule )
[May 18th]
[May 25th]
[Jun. 1st] No lecture (due to the university schedule )
[Jun. 2nd (Tuesday)]
[Jun. 8th]
[Jun. 15th]
[Jun. 22nd]
[Jun. 29th]
[Jul. 6th]
[Jul. 13th]
[Jul. 20th] No lecture (due to the national holiday)
[Jul. 27th]
Reports
Report I (deadline: 26th April 2026)
Report II (deadline: 31st May 2026)
Report III (deadline: XXth July 2026)
References
[Textbooks]
C. Itzykson & J.-M. Drouffe,
“Statistical Field Theory (Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory)”
(Cambridge University Press, Cambridge, England, 1989)
N. Goldenfeld,
“Lectures on Phase Transitions and the Renormalization Group”
(Westview Press, Boulder, CO, 1992)
J. Cardy,
“Scaling and Renormalization in Statistical Physics”
(Cambridge University Press, Cambridge, England, 1996)
M. Kardar,
“Statistical Physics of Fields”
(Cambridge University Press, Cambridge, England, 2007)
高橋 和孝・西森 秀稔、『相転移・臨界現象とくりこみ群』 (丸善出版、2017 年)
[Others]
K. G. Wilson, “The renormalization group and critical phenomena”, Rev. Mod. Phys. 55 , 583 (1983)
田崎 晴明、「くりこみ群とはなにか」[パリティ(1996 年 6 月) ]
D. Ashton, "The Renormalisation Group" (April 23rd, 2012)
J. Cardy, “The Legacy of Ken Wilson”, J. Stat. Mech. 2013 , P10002
[arXiv:1308.1785 ]
D. Tong, “Statistical Field Theory” (University of Cambridge Part III Mathematical Tripos, 2017)
X. Chen, “Essay: Generalized Landau Paradigm for Quantum Phases and Phase Transitions”, Phys. Rev. Lett. 135 , 250001 (2025)