Navigation
Advanced Statistical Physics (MVSpec)
Dozent: Prof. Dr. Tilman Enss
50 Teilnehmer/innen
This advanced theory lecture builds on the statistical physics course (MKTP1) and introduces paradigmatic models of statistical physics and their critical properties near phase transitions. In particular, we shall discuss the Heisenberg and O(N) vector models, the nonlinear sigma model, the XY model, the Sine-Gordon model, and the spherical model. By computing their critical behavior, one can understand the phase transitions in many different systems in statistical physics, condensed matter physics and beyond, which belong to the same universality classes. We will use field theoretic methods and introduce renormalization, epsilon expansion, and duality transformation.
Contents
- Landau theory and O(N) vector model
- Renormalization group and universality
- Nonlinear sigma model and epsilon expansion
- Topological excitations in the XY and Sine-Gordon models and the Berezinskii-Kosterlitz-Thouless transition
- Spherical model and quantum phase transitions
- Disordered systems
- Random walks
- Critical dynamics
Dates and Times
Lecture Tuesdays and Thursdays 11.15-13.00h in Philosophenweg 12, room 106
Tutorial Mondays 14.15-16.00h in Philosophenweg 12, large auditorium gHS
Timeline
2025-10-14: Lecture 1, Landau theory and mean field ansatz
2025-10-16: Lecutre 2, Fluctuations beyond mean field
2025-10-20: Tutorial 1, Correlations
2025-10-21: Lecture 3, O(N) and phi^4 models; scaling and renormalization
2025-10-23: Lecture 4, Renormalization group equations
2025-10-27: Tutorial 2, Ginzburg criterion
2025-10-28: Lecture 5, Relevance and universality
2025-10-30: Lecture 6, Multiple fixed points
2025-11-03: Tutorial 3, Flow equations
2025-11-04: Lecture 7, Nonlinear sigma model
2025-11-06: Lecture 8, Renormalization of the NLSM
2025-11-10: Tutorial 4, Limit cycles
2025-11-11: Lecture 9, XY model and spin waves
2025-11-13: Lecture 10, Vortices and Coulomb gas
2025-11-17: Tutorial 5, Duality
2025-11-18: Lecture 11, Sine-Gordon model and Berezinskii-Kosterlitz-Thouless transition
2025-11-20: Lecture 12, Quantum phase transitions
2025-11-24: Tutorial 6, BKT scaling
2025-11-25: Lecture 13, Random systems
2025-11-27: no lecture
2025-12-01: Tutorial 7, Quantum scaling
2025-12-02: Lecture 14, Random systems: renormalization
2025-12-04: Lecture 15, Spin glasses
2025-12-08: Tutorial 8, Disorder
2025-12-09: Lecture 16, Replica symmetry breaking
2025-12-11: Lecture 17, Neural networks and Anderson localization
2025-12-15: Tutorial 9, Random Process
2025-12-16: Lecture 18, Random walks: mapping to O(n) model
2025-12-18: Lecture 19, Random walks: critical scaling
Christmas break
2026-01-08: Lecture 20, Fluctuation-dissipation relation and Langevin equation
2026-01-12: Tutorial 10, Percolation (example code)
2026-01-13: Lecture 21, Master equation and response functional
2026-01-15: Lecture 22, Directed percolation and transport equations (lecture notes up to page 8-17)
2026-01-19: Tutorial 11, Stochastic dynamics
2026-01-20: Lecture 23, Fokker-Planck equation and approach to equilibrium [bonus material: functional renormalization]
2026-01-22: voluntary Question & Answer session in preparation for the exam
2026-02-10: written exam 10:00-11:30h (please register via HeiCO)
Literature
In this lecture we use the field theoretical language; for a recap see for instance Mudry chapter 1.For starters:
- Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press (1996)
- Mudry, Lecture Notes on Field Theory in Condensed Matter Physics, World Scientific (2014)
Further reading:
- Altland and Simons, Condensed Matter Field Theory, Cambridge University Press (2010)
- Di Castro and Raimondi, Statistical Mechanics and Applications in Condensed Matter, Cambridge University Press (2015)
- Kadanoff, Statistical Physics: statics, dynamics and renormalization, World Scientific (2000)
- Negele and Orland, Quantum Many-Particle Systems, Addison-Wesley (1988)
- Sachdev, Quantum Phase Transitions, Cambridge University Press (2011)
- Stein and Newman, Spin Glasses and Complexity, Princeton University Press (2013)
- Zinn-Justin, Phase Transitions and Renormalization Group, Oxford University Press (2007)
Übungsgruppen
- Gruppe 1 (T. Enss)
41 Teilnehmer/innen
Phil 12 gHS, Mo 14:15 - 16:00
