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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.
Last update: T_UTF (15.05.2014)
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Ústní zkouška Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)
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M. Plischke and B. Bergensen, Equilibrium statistical physics, World Scientific, Singapore, 1994 (2. vydání) K. Huang, Statistical mechanics, John Wiley & Sons, Singapore, 1987 (2. vydání) G. Parisi, Statistical field theory, Addison Wesley, New York, 1988 C. Itzykson and J.-M. Drouffe, Statistical field theory, vol. 1, Cambridge UP, Cambridge, 1989 J. Cardy, Scaling and renormalization in statistical physics, Cambridge UP, Cambridge, 1996 K. B. Effetov: Advances in Physics 32 (1983) 53. M. E. J. Newman, Networks, Oxford UP, Oxford, 2010
Last update: Kotrla Miroslav, RNDr., CSc. (13.05.2011)
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Zkouška je ústní, požadavky odpovídají sylabu, v detailech pak tomu, co bylo během semestru odpřednášeno. Last update: Houfek Karel, doc. RNDr., Ph.D. (11.06.2019)
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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 Last update: SLANINA/MFF.CUNI.CZ (07.06.2012)
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