Infopaket

Statistical quantum field theory

ОК 5

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

1. Know the basics of the theory of critical phenomena, the theory of the mean field and the problems of taking into account the interaction of fluctuations of the order parameter. 2. Know the basic methods of applying the Feynman integral to the description of fluctuations of the order parameter and the relationship between the physics of critical phenomena and the application of quantum field theory in the theory of phase transitions. 3. Be able to apply thermodynamics, methods of statistical physics and middle field theory to describe critical phenomena in magnetic systems. 4. Be able to apply the methods of quantum field theory to take into account the interaction of fluctuations of the order parameter in the vicinity of the critical point in the Ising model.

Full-time form

1. Know the basics of functional integral technique in quantum field theory and statistical mechanics, basic concepts of physics of quantum systems of many particles and statistical physics. 2. To be able to apply previously acquired knowledge from the courses of condensed matter physics, statistical physics of lattice systems and systems of many particles to solve practical problems. 3. Possess basic skills of calculations in the course of Feynman integral in quantum mechanics, quantum field theory and statistical physics, independent use and study of the literature on statistical physics and condensed matter physics.

1. Phenomenological theory of the Ginsburg-Landau mean field. 2. Ising model and Ginzburg-Landau theory. 3. Ginzburg-Landau theory for an inhomogeneous order parameter. 4. Calculation of asymptotics of correlation functions in the theory of Ginzburg-Landau. 5. Effective field theory of the interaction of order parameter fluctuations in the Ising model. 6. Field method of generating functionals for calculating thermodynamic potentials in the Ising model. 7. Obtaining the Ginzburg-Landau mean field theory from the effective field theory of the interaction of fluctuations of the order parameter. 8. Ginzburg-Levanyuk criterion.

1. Huang K. Introduction to Statistical Physics. – Boca Raton: Chapman & Hall/CRC, 2010. – 318 p. 2. Lesne A., Lagües M. Scale Invariance: From Phase Transitions to Turbulence. – Berlin: Springer-Verlag, 2012. – 400 p. 3. Zinn-Justin J. Phase Transitions and Renormalisation Group. – Oxford: Oxford University Press, 2007. – 465 p. 4. Mussardo G. Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics. – Oxford: Oxford University Press, 2009. – 778 p. 5. Nishimori H., Ortiz G. Elements of phase transitions and critical phenomena. – Oxford: Oxford University Press, 2011. – 358 p. 6. Brezin E. Introduction to statistical field theory. Cambridge: Cambridge University Press, 2010. – 178 p. 7. Сhaikin P.M., Lubensky N.C. Principles of condensed matter physics. – Cambridge: Cambridge University Press, 2000. – 720 p.

Lectures, practical classes, independent work.

Oral responses, modular tests, control of practical work, examination work.

Ukrainian