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Modern Applications of Statistical Physics II - NTMF050

Title:	Moderní aplikace statistické fyziky II
Guaranteed by:	Institute of Theoretical Physics (32-UTF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://otokar.troja.mff.cuni.cz/vyuka/sylaby/sylaby.htm

Guarantor:	RNDr. František Slanina, CSc. RNDr. Miroslav Kotrla, CSc.
Classification:	Physics > Theoretical and Math. Physics
Co-requisite :	NTMF049

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_UTF (15.05.2014)

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.

Course completion requirements - Czech

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Ústní zkouška

Literature - Czech

Last update: RNDr. Miroslav Kotrla, CSc. (13.05.2011)

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

Requirements to the exam - Czech

Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Zkouška je ústní, požadavky odpovídají sylabu, v detailech pak tomu, co bylo během semestru odpřednášeno.

Syllabus -

Last update: SLANINA/MFF.CUNI.CZ (07.06.2012)

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