The non-Fermi-liquid (NFL) behavior observed in the low temperature specific heat C(T ) and magnetic susceptibility χ(T ) of f-electron systems is analyzed within the context of a recently developed theory based on Griffiths singularities. Measurements of C(T ) and χ(T ) in the systems Th1−xUxPd2Al3, Y1−xUxPd3, and UCu5−xMx (M = Pd, Pt) are found to be consistent with C(T )/T ∝ χ(T ) ∝ T −1+λ predicted by this model with λ < 1 in the NFL regime. These results suggest that the NFL properties observed in a wide variety of f-electron systems can be described within the context of a common physical picture. PACS: 71.27+a, 75.20.Hr, 71.10.Hf Transport, thermal, and magnetic measurements on a number of chemically substituted rare earth and actinide compounds have revealed low temperature physical properties that show striking departures from the predictions of Fermi-liquid theory [1]. Several theoretical models have been developed to account for the non-Fermi-liquid (NFL) behavior observed in f-electron materials. These models include a multichannel Kondo effect of magnetic or electric origin [2-4], fluctuations of an order parameter in the vicinity of a second order phase transition at T = 0 K [5-7], a disordered distribution of Kondo temperatures [8,9], and an electron polaron model for heavy fermion systems [10]. However, none of these models has been able to account for all of the NFL characteristics observed in the wide variety of systems that belong to this new class of strongly correlated f-electron materials. Three of us (A. H. C. N., G. E. C., and B. A. J.) have recently proposed a model where NFL behavior is associated with the proximity to a quantum critical point and the formation of magnetic clusters in the paramagnetic phase due to the competition between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in the presence of magnetic anisotropy and disorder inherent in alloyed materials [11]. This model predicts that various physical properties diverge with decreasing temperature as weak power laws of temperature and that this behavior persists over appreciable ranges of substituent concentration, similar to what has been observed in a number of f-electron materials.

Certain chemically substituted Ce and U compounds have low-temperature physical properties that exhibit non-Fermi-liquid (NFL) characteristics and apparently constitute a new class of strongly correlated f-electron materials. The NFL behaviour takes the form of weak power law or logarithmic divergences in the temperature dependence of the physical properties that scale with a characteristic temperature , which, in some systems, can be identified with the Kondo temperature . These systems have complex temperature T - chemical substituent composition x phase diagrams, which contain regions displaying the Kondo effect, NFL behaviour, spin glass freezing, magnetic order, quadrupolar order, and, sometimes, even superconductivity. Possible origins of the NFL behaviour include a multichannel Kondo effect and fluctuations of an order parameter in the vicinity of a second-order phase transition at T = 0 K. Recent experiments on the systems and are reviewed. In the and systems, the low-temperature physical properties in the NFL regime scale with the U concentration and , suggesting that single-ion effects are responsible for the NFL behaviour.