Quantum phase transitions

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Phase transitions which occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed are called quantum phase transitions. They are caused by quantum fluctuations which are a consequence of Heisenberg's uncertainty principle. These lecture notes give a pedagogical introduction to quantum phase transitions. After collecting a few basic facts about phase transitions and critical behavior we discuss the importance of quantum mechanics and the relation between quantum and classical transitions as well as their experimental relevance. As a primary example we then consider the Ising model in a transverse field. We also briefly discuss quantum phase transitions in itinerant electron systems and their connection to non-Fermi liquid behavior.