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 guassian field h(t),

~ 1 over t sup (2-epsilon) with small positive epsilon. In absence of and additional Kondo coupling, I get power-law decay of spin correlators, ~ 1 over t sup (epsilon). For negative epsilon, the spin autocorrelation in 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.