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Spin and gauge models in lattice field theory

ОК 9

Обов’язкова дисципліна для ОП

Second

2018/2019

2 Semester

3

Know the main properties of spin models with ferromagnetic interaction and perturbative lattice theory. Know the calibration theories on the lattice and their properties, three-dimensional Abelian calibration theories, and the basics of non-Abelian calibration theories. Be able to calculate the mass gap for Abelian and non-Abelian models and perturbative calculation of free energy. Be able to solve two-dimensional calibration theories.

Full-time form

1. Know statistical mechanics, basic principles of calibration theories, critical theory phenomena and phase transitions, perturbative quantum field theory. 2. Be able to apply methods of asymptotic decompositions of multidimensional integrals.

1. Introduction to the lattice model. 2. Methods of plasma description Properties of spin models with ferromagnetic interaction. One-dimensional spin models. 3. Two-dimensional XY-model. 4. Perturbative theory on the lattice. 5. Two-dimensional non-Abelian models. 6. Calibration theories on the lattice and their properties. 7. Solving two-dimensional calibration theories. 8. Three-dimensional Abelian calibration theories. Fundamentals of non-Abelian calibration theories.

1. C. Itzykson, J. M.Drouffe. Statistical field theory. Volume 1 and 2, Cambridge University Press, 2012. 2. J. Kogut. An introduction to lattice gauge theory and spin systems, Rev.Mod.Phys. -1979. -Volume 51, No4. -P.659-713. 3. H. J. Rothe, Lattice Gauge Theories: An Introduction, World Scientific Publishing Company; 4th edition., 2012.

Lectures, practical classes, independent work.

Current survey, modular test, test work.

Ukrainian