Critical local moment fluctuations in the Bose-Fermi Kondo model

We study the critical properties of the Bose-Fermi Kondo model, which describes a local moment coupled simultaneously to a conduction electron band and a fluctuating magnetic field (a dissipative bath of vector bosons). We carry out an $\epsilon=1-\gamma$-expansion, where $\gamma$ is an exponent characterizing the spectrum of the fluctuating magnetic field, to higher than linear orders. We calculate the local susceptibility at the unstable critical point of this model to the order $\epsilon ^ 2$ and, in addition, determine the associated critical exponent to all orders in $\epsilon$. We also discuss the effect of anisotropy in the spin space. Our main result is that the critical exponent for the local spin susceptibility at an unstable fixed point is equal to $\epsilon$ in all these different cases. Our results imply that a locally critical point of the Kondo lattices is self-consistent to all orders in $\epsilon$.