University of Cologne // Institute for Theoretical Physics

Exercise class
Advanced Statistical Physics Winter Semester 2017-2018

Lecture
Prof. Johannes Berg
Excercises
Dr. Simone Pompei (pompei@thp.uni-koeln.de)

Tutorials

Hand-in
Exercises are to be thrown into the mailbox in front of the theory institute.
Reading
Copies of the relevant book parts can be found in the library of the physics department (please ask Mrs. Ute Graffenberger).

Group  Time Place Tutor e-mail
I Monday 1200-1330   SR II  Stephan Kleinbölting  skleinbo@thp.uni-koeln.de
II Monday 1600-1730   SR I  Nina Müller  nina.mueller@uni-koeln.de
III Monday 1745-1915   SR I  Ulrich Michel  um@thp.uni-koeln.de
IV Monday 800-930   0.02 New Building  Mara Villa  mvilla@uni-koeln.de

Problem sets

Exercise 1 Reading assignment from N.G. Van Kampen, Stochastic Processes in Physics and Chemistry.

Read:
  • Chapter 1 (Stochastic Variables)
  • Sections 2.1-2.2 (Random events: (i) Definition (ii) The Poisson Distribution)
  • Sections 3.1-3.2 (Stochastic Processes: (i) Definition (ii) Stochastic processes in physics)
  • Sections 4.1-4.2-4.3 (Markov Processes: (i) The Markov Property (ii) The Chapman Kolmogorov Equation (iii) Stationary Markov process)
Exercise 2 Reading assignment from N.G. Van Kampen, Stochastic Processes in Physics and Chemistry + Problem set 1

  • Read: Chapter 5, Sections 5.1-5.4 (The Master Equation: (i) Derivation (ii) The class of W matrices (iii) The long time limit (iv) Closed, isolated, physical systems )
  • The text of the problem set has been slightly modified! Re-download it please!
    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 24/10/2017. The solutions will be discussed in the exercise class of Monday 30/10/2017.
Exercise 3 Problem set 2.

    27/10/2017. Typo fixed: Re-download it please!
    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the exercise class on Monday 30/10/2017. The solutions will be discussed in the exercise class of Monday 6/11/2017.
Exercise 4 Problem set 3.


    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 7/10/2017. The solutions will be discussed in the exercise class of Monday 13/11/2017.
Exercise 5 Reading assignment from N. Goldenfeld, Lectures on phase transitions and the renormalization group + Problem set 4

  • Read: Chapter 2, Sections 2.1-2.9 (How Phase Transitions Occur In Principle: (i) Review of Statistical Mechanics (ii) The Thermodynamic Limit (iii) Phase Boundaries and Phase Transitions (iv) The Role of Models (v) The Ising Model (vi) Analytic Properties of The Ising Model (vii) Symmetry Properties of the Ising Model (viii) Existence of Phase Transitions (ix) Spontaneous Symmetry Breaking )
  • 10/11/2017. Typo fixed: Re-download it please!
    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 14/11/2017. The solutions will be discussed in the exercise class of Monday 20/11/2017.
Exercise 6 Reading assignment from M. Kardar, Statistical Physics of Fields+ Problem set 5

  • Read: Chapter 7, Sections 7.1-7.4 (Series Expansions: (i)Low-temperature expansions (ii) High-temperature expansions (iii) Exact solution of the one-dimensional Ising-model (iv) Self-duality of the two-dimensional Ising model)
  • Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 21/11/2017. The solutions will be discussed in the exercise class of Monday 27/11/2017.
Exercise 7 Problem set 6.


    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 28/11/2017. The solutions will be discussed in the exercise class of Monday 4/12/2017.
Exercise 8 Reading assignment from M. Kardar, Statistical Physics of Fields (2 weeks time) + Problem set 7

  • Read (2 weeks time): Chapter 2, Sections 2.1-2.3 (Statistical Fields : (i) Introduction (ii) The Landau-Ginzburg Hamiltonian (iii) Saddle point approximation, and mean field theory) Chapter 3, Sections 3.5-3.6 (Flutctuations : (v) Gaussian integrals (vi) Fluctuation corrections to saddle point)
  • 28/11/2017 evening. A julia template is also available: see the new link in the Problem set: the exercise can be downloaded from  here . Please send your code together with the outputs, figures to the tutor of your group of exercise before the 5/12/2017. The solutions will be discussed in the exercise class of Monday 11/12/2017.
Exercise 9 Problem set 8.


    Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 12/12/2017. The solutions will be discussed in the exercise class of Monday 18/12/2017.
Exercise 10 Reading assignment from J. Cardy, Scaling and Renormalization in Statistical Physics + Problem set 9

  • Read: Chapter 3, Sections 3.1-3.3 (The Renormalization group idea: (i) Block spin transformations (ii) One-dimensional Ising model (iii) General theory)
  • Problem set: the exercise can be downloaded from  here . The deadline to hand this exercise in is at the end of the class lecture on Tuesday 19/12/2017. The solutions will be discussed in the exercise class of Monday 8/01/2018.

Literature

  • N. Goldenfeld, Lectures on phase transitions and the renormalization group, Westview Press
  • N.G. van Kampen, Stochastic Processes in Physics and Chemistry, North Holland
  • M. Kardar, Statistical Physics of Fields, Cambridge University Press
  • J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press
  • M. Plischke and B. Bergersen, Equilibrium Statistical Physics, World Scientific
  • (in German) H. Römer and T. Fink, Statistische Mechanik, VCH