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 $h\left(t\right),$ $〈\mathrm{Th}\left(t\right)h\left(0\right)\mathrm{}〉\sim {1/t}^{2-\epsilon }$ with small positive $\epsilon .$ In the absence of any additional Kondo coupling, I get power-law decay of spin correlators, $〈\mathrm{TS}\left(t\right)S\left(0\right)\mathrm{}〉\sim {1/t}^{\epsilon }.$ For negative $\epsilon ,$ 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.