  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 renormalisation group flows for these
models have controlled fixed points when the autocorrelation of the gaussian
field $h(t)$, $<T h(t) h(0)> \sim {1\over t^{2-\epsilon}}$ with small positive
$\epsilon$. In absence of any additional Kondo coupling, I get powerlaw decay
of spin correlators, $<T S(t) S(0)> \sim {1\over t^{\epsilon}}$ . 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 behaviour 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.
