Advanced Statistical Physics

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

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. 

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)

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

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

Participation in the exercise classes 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 the successful completion of at least 50% of the homework exercises.