Syllabus
Methods of field theory in satisical physics
Landau-Ginzburg model, expansion in interaction parameter, diagrammatic series, resummations, Dyson equation
Disordered systems percolation, magnetic material in random magnetic field, replica method, supersymmetric methods, random matrices, quantum particle in random potential
Renormalization group change of scale, renormalization flow, fixed points (stable, unstable, mixed), proof of scaling hypothesis, extyraction of critical exponents, proof of scaling relations, real-space renormalization group, momentum-space renormalization group, diagrams, epsilon-expansion
Network theory
Erd's-Rényi model, small worlds, scale-free networks, robustness of networks, examples: internet, social networks, power grids
Annotation
We shall cover some more advanced topics of statistical physics, especially the diagrammatic techniques. First we introduce applications of field theory in statistical physics and then we deal with disordered systems. To this end we show the replica method and the use of supersymmetry. Then we explain the renormalization group method for computing critical exponents. Another topic will be the theory of complex networks with an application for example on the internet.
This lecture is intended for master and docoral students.