Fakultät > Vorlesungen > Wintersemester 2024/2025 > Advanced Statistical Physics (MVSpec)

Advanced Statistical Physics (MVSpec)

Wintersemester 2024/2025
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

  1. Landau theory and O(N) vector model
  2. Renormalization group and universality
  3. Nonlinear sigma model and epsilon expansion
  4. Topological excitations in the XY and Sine-Gordon models and the Kosterlitz-Thouless transition
  5. Spherical model and quantum phase transitions
  6. Disordered systems
  7. Random walks
  8. 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, RKKY

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)
  • 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)
  • Zinn-Justin, Phase Transitions and Renormalization Group, Oxford University Press (2007)

Übungsblätter

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Advanced Statistical Physics (MVSpec)
Wintersemester 2024/2025
Enss T
43 Teilnehmer/innen
Termine