Quantum critical fluctuations in layered YFe2Al10

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Quantum critical phenomena

John Hertz (1976)

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Effect of a nonzero temperature on quantum critical points in itinerant fermion systems

A. Millis (1993)

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Fermi-liquid instabilities at magnetic quantum phase transitions

Matthias Vojta, Peter Wölfle, Hilbert Löhneysen … (2006)

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.