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Advanced Statistical Physics II Winter 2021/2022

Participation: registration in Campus Management required

General information: pdf

Lectures: Mo, Wed 10:15-12:00, Hörsaal A

Tutorials: Fr 14-16 (1.4.03 Seminarraum T2)

Content: Selected topic in statistical physics, in particular theory of phase transitions (Landau theory, Gaussian fluctuations, correlation functions, renormalization group)

Prerequisites: Good knowledge of thermodynamics and statistical mechanics (e.g., Advanced Statistical Mechanics I or equivalent)

Problem sets: published online on this webpage on Mondays, must be submitted the following Monday before the beginning of class; active participation will require 50% of points

Exam: written exam on course material on Mo, Feb 28, 2022, 10-12am  HÖRSAAL A!

Second exam: Friday, April 22, 2022, 10-12am, room to be announced (please register by email to instructor if you plan to take the exam)  

Problem Sets:

Set 1          solution

Set 2          solution

Set 3          solution

Set 4          solution

Set 5          solution

Set 6          solution

Set 7          solution         

Set 8          solution

Set 9          solution

Set 10        see lecture notes

Set 11        solution

Set 12        see lecture notes

Class notes:

Chapter 1    Phases and phase transitions, models (Ising, xy, n-vector), structure and scattering, elasticity

Chapter 2    Review of thermodynamics and statistical physics

Chapter 3  Mean field theory: applications to magnetic systems, simple fluids, and liquid crystals, Landau theory and critical exponents, variational mean field theory

Chapter 4   Fluctuations: Landau functional, Ginzburg criterion, loop expansion, Hartree approximation

Chapter 5  Scaling relations, real-space RG

Chapter 6  Field theory formulation of (momentum-space) RG:  epsilon expansion, crossover, n-vector model with cubic anisotropy

Chapter 7  Elastic theories: non-linear sigma model and 2+epsilon expansion, xy model and topological defects, Kosterlitz-Thouless transition, real-space RG, momentum-space RG, and sine-Gordon model

Chapter 8  Growth models: Langevin and Fokker Planck equations, Edwards-Wilkinson equation, Kardar-Parisi-Zhang equation, RG treatment