Non-Fermi Liquid Behavior in U and Ce Alloys: Criticality, Disorder, Dissipation, and Griffiths-McCoy singularities
In this paper we provide the theoretical basis for the problem of Griffiths-McCoy singularities close to the quantum critical point for magnetic ordering in U and Ce intermetallics. We show that the competition between Kondo effect and RKKY interaction can be expressed in Hamiltonian form and the dilution effect due to alloying leads to a quantum percolation problem driven by the number of magnetically compensated moments. We argue that the exhaustion paradox proposed by Nozières is explained when the RKKY interaction is taken into account. We revisited the one impurity and two impurity Kondo problem and showed that in the presence of particle-hole symmetry breaking operators the system flows to a line of fixed points characterized by coherent motion of the spins. This leads to a {\it cluster Kondo effect}. We calculate explicitly from the microscopic Hamiltonian the parameters which appear in all the response functions. We show that there is a maximum number $N_c$ of spins in the clusters such that above this number tunneling ceases to occur. These effects lead to a distribution of cluster Kondo temperatures which vanishes for finite clusters and therefore leads to strong magnetic response. From these results we propose a {\it dissipative quantum droplet model} which describes the critical behavior of metallic magnetic systems. This model predicts that in the paramagnetic phase there is a crossover temperature $T^*$ above which Griffiths-McCoy like singularities with power law behavior. Below $T^*$, however, a new regime dominated by dissipation occurs with stronger divergences. We estimate that $T^*$ is exponentially small with $N_c$.