  We study the single channel (compactified) models, the sigma-tau model and
the O(3) symmetric Anderson model, which were introduced by Coleman et al., and
Coleman and Schofield, as a simplified way to understand the low energy
behaviour of the isotropic and anisotropic two channel Kondo systems. These
models display both Fermi liquid and marginal Fermi liquid behaviour and an
understanding of the nature of their low energy fixed points may give some
general insights into the low energy behaviour of other strongly correlated
systems. We calculate the excitation spectrum at the non-Fermi liquid fixed
point of the sigma-tau model using conformal field theory, and show that the
results are in agreement with those obtained in recent numerical
renormalization group (NRG) calculations. For the O(3) Anderson model we find
further logarithmic corrections in the weak coupling perturbation expansion to
those obtained in earlier calculations, such that the renormalized interaction
term now becomes marginally stable rather than marginally unstable. We derive a
Ward identity and a renormalized form of the perturbation theory that
encompasses both the weak and strong coupling regimes and show that the
chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin),
independent of the interaction U and in agreement with the NRG calculations.
