Navigation
Advanced Statistical Physics (MVSpec)
Dozent: Prof. Dr. Tilman Enss
43 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, room 070
written exam on Thursday 30 January 2025, 11-13h (registration via HeiCO required)
Timeline
2024-10-15: Lecture 1, Landau theory and mean field ansatz
2024-10-17: Lecutre 2, Fluctuations beyond mean field
2024-10-21: Tutorial 1, Correlations
2024-10-22: Lecture 3, O(N) and phi^4 models; scaling and renormalization
2024-10-24: Lecture 4, Renormalization group equations
2024-10-28: Tutorial 2, Ginzburg criterion
2024-10-29: Lecture 5, Relevance and universality
2024-10-31: Lecture 6, Multiple fixed points
2024-11-04: Tutorial 3, Flow equations
2024-11-05: Lecture 7, Nonlinear sigma model
2024-11-07: Lecture 8, Renormalization of the NLSM
2024-11-11: Tutorial 4, Limit cycles
2024-11-12: Lecture 9, XY model and spin waves
2024-11-14: Lecture 10, Vortices and Coulomb gas
2024-11-18: Tutorial 5, Duality
2024-11-19: Lecture 11, Sine-Gordon model
2024-11-21: Lecture 12, Berezinskii-Kosterlitz-Thouless transition
2024-11-25: Tutorial 6, BKT scaling
2024-11-26: Lecture 13, Quantum phase transitions
2024-11-28: Lecture 14, Random systems
2024-12-02: Tutorial 7, Quantum scaling
2024-12-03: Lecture 15, Random systems: renormalization
2024-12-05: Lecture 16, Spin glasses
2024-12-09: Tutorial 8, Disorder
2024-12-10: Lecture 17, Replica symmetry breaking
2024-12-12: Lecture 18, Neural networks and Anderson localization
2024-12-16: Tutorial 9, Duality II
2024-12-17: Lecture 19, Random walks: mapping to O(n) model
2024-12-19: Lecture 20, Random walks: critical scaling
Christmas break
2025-01-07: Tutorial 10, Percolation (NOTE: TUTORIAL DURING LECTURE TIME)
2025-01-09: Lecture 21, Fluctuation-dissipation relation and Langevin equation
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
36 Teilnehmer/innen
Phil 12 070, Mo 14:15 - 16:00
