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Introduction to Renormalization

Introduction to Renormalization with Applications in Condensed-Matter and High-Energy Physics Institute for Theoretical Physics, University of Cologne Lecture course, winter term 2017/2018. Michael M. Scherer January 26, 2021. Contents Contents 1. 1 Introduction 5. Aspects of the Renormalization group .. 6. Phase transitions .. 7. Critical phenomena .. 8. Perturbative quantum field theory .. 9. Renormalization -group based definition of QFTs .. 10. QFTs in the high-energy limit .. 11. 2 Phase transitions and critical phenomena 13. Ising model .. 13. Remarks on solutions of the Ising model in d = 1 and d = 2 .. 14. Symmetries of the Ising model .. 15. XY model and Heisenberg model .. 15. Universality and critical exponents .. 16. Scaling hypothesis for the free energy .. 17.

The renormalization group refers to a mathematical procedure that facilitates the system- atic study of the changes of a physical system when viewed at di erent length or energy scales.

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