These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.
T. Vojta, "Phases and Phase Transitions in Disordered Quantum Systems," AIP Conference Proceedings, vol. 1550, pp. 188 - 247, American Institute of Physics (AIP), Oct 2013.
The definitive version is available at https://doi.org/10.1063/1.4818403
17th Training Course in the Physics of Strongly Correlated Systems (2012: Oct. 1-12, Salerno, Italy)
Keywords and Phrases
critical point; disorder; Griffiths singularity; phase transition; renormalization group
International Standard Book Number (ISBN)
International Standard Serial Number (ISSN)
Article - Conference proceedings
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01 Oct 2013