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Advanced Statistical Physics

Module PH2260

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2021/2 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2WS 2020/1WS 2019/20WS 2017/8

Basic Information

PH2260 is a semester module in German or English language at Master’s level which is offered in winter semester.

This module description is valid from WS 2017/8 to SS 2022.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
300 h 90 h 10 CP

Responsible coordinator of the module PH2260 is Johannes Knolle.

Content, Learning Outcome and Preconditions


  • Phase Transitions and Critical Phenomena
  • Landau-Ginzburg Theory and Fluctuations
  • Renormalization Group (Basics and Applications)
  • Irreversible Processes and Non-Equilibrium Phenomena
  • Percolation

Learning Outcome

After successful completion of the module the students are able to:

  1. Explain the concept of critical phenomena and analyse them with the help of critical exponents
  2. Understand the use and methodology of the renormalisation group approach
  3. Analyse a given system using the renormalisation group approach
  4. Explain the Ginzburg-Landau theory and apply the renormalisation group approach to it
  5. Explain and compare different approaches of non-equilibrium physics
  6. Understand the basic principles of percolation and non-equilibrium universality


Familiarity with the basic concepts of statistical physics on bachelor level (PH0008) is required. 

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

This module consists of a lecture and an exercise class.

In the thematically structured lecture the theoretical contents are presented and discussed. The relevant experimental results for phase transitions, non-equilibrium phenomena and the theory of percolation are presented. The theoretical models for their description are developed in the lectures together with the students. Solution- and approximation methods like the renormalization group approach for phase transitions are presented and discussed in detail. A dialogical structure of the lecture is emphasized to advance the analytic-physics intellectual power of the students and to encourage a critical scrutinization of the chosen approaches.

In the problem sets the students have the opportunity to apply the presented techniques to concrete problem examples and to analyze the results. In the course of this analytic calculation exercises, simple numerical simulations and conceptual questions with answers in the form of continuous text are chosen as task form. The solution proposals of the students are corrected to give the students feedback for their modeling and solution abilities and to detect and correct misconceptions as early as possible. 

In the exercises the solutions of the problem sets are presented as well as common misconceptions. Furthermore, specific topics of the lecture are discussed in-depth and relevant aspects are reviewed in regular intervals. Questions of students are given a large space.


Lectures will be held online and lecture recordings will be available

A script of the lectures is provided, notes for each individual lecture will be uploaded

There will be both in-person and online tutorials available for discussing the exercises


  • M. Kardar: Statistical Physics of Fields, Cambridge University Press, (2007)
  • K. Christensen and N. R. Moloney: Complexity and Criticality, Imperial College Press, (2005)
  • M. Le Bellac, F. Mortessagne,  G.G. Batrouni: Equilibrium and Non-Equilibrium Statistical Thermodynamics, Cambridge University Press, (2004)
  • M. Kardar: Statistical Physics of Particles, Cambridge University Press, (2007)

Module Exam

Description of exams and course work

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Analyse the Ginzburg-Landau theory with the renormalisation group approach.
  • Explain the concept of a critical exponent.

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of solving at least 70% of the homework problems.

Exam Repetition

The exam may be repeated at the end of the semester.

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