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294 Handbook on the Physics and Chemistry of Rare Earths ordered state at zero temperature to a new quantum phase. Such a zero tem- perature phase transition leads to a dramatic change of the electronic proper- ties at finite, nonzero temperatures. There are many good reviews on QPTs, for example, Pfleiderer (2009), Gegenwart et al. (2008), Sachdev (2008), and von L€ohneysen et al. (2007). Unlike those reviews we will not be complete in the enumeration of all measured properties of all possible quantum critical compounds. Instead, we want to provide a critical view on QPTs in certain prototype rare earth and actinide-based compounds. The concept of quantum criticality, which we will discuss in-depth in Section 2, has lead to a surge of novel concepts, most important of them is scaling. Scaling suggests that many measurable quantities, such as the specific heat coefficient, the thermal expansion, and magnetic susceptibility, have sim- ple power-law behavior as a function of temperature, pressure, or magnetic field. Indeed, some materials are fully described the scaling laws as derived by the theory of Hertz, Millis, and Moriya. However, it was soon found that many materials—such as Ce(Cu,Au)6 and YbRh2Si2—not only violate FL theory, but also Hertz–Millis (HM) theory. After presenting these compounds, we elaborate in Section 3 on the short- comings of HM theory and list recent attempts toward better theories. In line with our philosophy, we will review those theories critically: unfortunately, many of them are either based on unquantifiable assumptions or lack a micro- scopic derivation. Nonetheless, the conceptual power of quantum criticality still stands, and the novel non-Fermi liquid (NFL) materials Ce-115 and URu2Si2 are looked at through quantum critical glasses. By discussing difficulties associated with “hidden” quantum critical points (QCPs), disorder, and material stability we aim to show in Section 4 the challenges and opportunities associated with using concepts from QPTs. Section 5 lists other forms of quantum matter beyond the rare earths and actinides. 2 HISTORICAL BACKGROUND 2.1 Classical Continuous Phase Transitions This chapter deals with phase transitions of a special kind, namely QCPs. Before delving into that topic, we need to review some general properties of phase transitions. Most phase transitions we encounter in daily life, like the liquid–gas or the freezing transition, are of the first order kind. First order transitions are characterized by a discontinuous change of the material proper- ties and release (or absorb) latent heat. Second order or continuous phase transitions (CPTs) are more subtle. No latent heat is involved, but the specific heat still displays nonanalytic behavior in the form of a divergence or a kink. In terms of the reduced temperaturePDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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