Spin in a fluctuating field: The Bose(+Fermi) Kondo models

I consider models with an impurity spin coupled to a fluctuating Gaussian field with or without additional Kondo coupling of the conventional sort. In the case of isotropic fluctuations, the renormalization-group flows for these models have controlled fixed points when the autocorrelation of the Gaussian field $h(t),$ 〈Th(t)h(0)〉~1/t^2-ε with small positive ε. In the absence of any additional Kondo coupling, I get power-law decay of spin correlators, 〈TS(t)S(0)〉~1/t^ε. For negative ε, the spin autocorrelation is constant in long-time limit. The results agree with calculations in Schwinger Boson mean-field theory. In presence of a Kondo coupling to itinerant electrons, the model shows a phase transition from a Kondo phase to a field fluctuation dominated phase. These models are good starting points for understanding behavior of impurities in a system near a zero-temperature magnetic transition. They are also useful for understanding the dynamical local mean-field theory of Kondo lattice with Heisenberg (spin-glass-type) magnetic interactions as well as for understanding spin-fluid solutions near Mott transition in t-J model.