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Advanced Statistical Physics
Dozent: Prof. Tilman Enss
Link zum LSF
7 Teilnehmer/innen
This advanced theory course 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 Kosterlitz-Thouless transition
- Spherical model and quantum phase transitions
- Disordered systems
- Random walks
- Critical dynamics
Timeline
2021-10-18: no tutorial (tutorial starts in the second week)
2021-10-19: Lecture 1, Landau theory and mean field ansatz
2021-10-21: Lecutre 2, Fluctuations beyond mean field
2021-10-25: Tutorial 1, Correlations
2021-10-26: Lecture 3, O(N) and phi^4 models; scaling and renormalization
2021-10-28: Lecture 4, Renormalization group equations
2021-11-01: no tutorial (public holiday)
2021-11-02: Lecture 5, Relevance and universality
2021-11-04: Lecture 6, Multiple fixed points
2021-11-08: Tutorial 2, Ginzburg criterion
2021-11-09: Lecture 7, Nonlinear sigma model
2021-11-11: Lecture 8, Renormalization of the NLSM
2021-11-15: Tutorial 3, Flow equations
2021-11-16: Lecture 9, XY model and spin waves
2021-11-18: Lecture 10, Vortices and Coulomb gas
2021-11-22: Tutorial 4, Limit cycles
2021-11-23: Lecture 11, Sine-Gordon model
2021-11-25: Lecture 12, BKT transition
2021-11-29: Tutorial 5, Duality
2021-11-30: Lecture 13, Quantum phase transitions
2021-12-02: Lecture 14, Random systems
2021-12-06: no tutorial (postponed)
2021-12-07: Lecture 15 (video), Random systems: renormalization
2021-12-09: Lecture 16, Spin glasses (up to page 6-12)
2021-12-13: Tutorial 6, Quantum scaling
2021-12-14: Lecture 17, Replica symmetry breaking (up to page 6-18)
2021-12-16: Lecture 18, Neural networks and Anderson localization (up to page 6-23)
2021-12-20: Tutorial 7, RKKY
2021-12-21: Lecture 19, Random walks (up to page 7-5)
Christmas break
2022-01-10: Tutorial 8, Percolation (example code)
2022-01-11: Lecture 20, Random walks (up to page 7-9)
2022-01-13: Lecture 21, Fluctuation-dissipation relation and Langevin equation (up to page 8-4)
2022-01-17: Tutorial 9, Random walks
2022-01-18: Lecture 22, Dynamical scaling and Master equation (up to page 8-9)
2022-01-20: Lecture 23, Response functional and directed percolation (up to page 8-14)
2022-01-24: Tutorial 10, Stochastic dynamics
2022-01-25: Lecture 24, Fokker-Planck equation and approach to equilibrium (up to page 8-19)
2022-02-08: voluntary Question & Answer session in preparation for the exam
2022-02-15: written exam
Literature
As an introduction, the lecture notes by Mudry are recommended; Mudry chapter 1 introduces the field theoretical language.
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)
- Kadanoff, Statistical Physics: statics, dynamics and renormalization, World Scientific (2000)
- Negele and Orland, Quantum Many-Particle Systems, Addison-Wesley (1988)
- 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)
7 Teilnehmer/innen
Philos.-weg 12 / R 105, Mo 14:15 - 16:00
