  The phase diagram of the multichannel Kondo Hamiltonian with an XXZ
spin-exchange anisotropy is revisited, revealing a far richer fixed-point
structure than previously appreciated. For a spin-1/2 impurity and k > 2
conduction-electron channels, a second ferromagnetic-like domain is found deep
in the antiferromagnetic regime. The new domain extends above a (typically
large) critical longitudinal coupling J_z^{\ast} > 0, and is separated from the
antiferromagnetic domain by a second Kosterliz-Thouless line. A similar line of
stable ferromagnetic-like fixed points with a residual isospin-1/2 local moment
is shown to exist for large J_z >> |J_{\perp}| > 0 and arbitrary k and s
obeying |k - 2s| > 1. Here J_z is the longitudinal spin-exchange coupling,
J_{\perp} is the transverse coupling, and s is the impurity spin. Near the
free-impurity fixed-point, spin-exchange anisotropy is a relevant perturbation
for s > 1/2 and arbitrary k. Depending on the sign of J_z^2 - J_{\perp}^2 and
the parity of 2s, the system flows either to a conventional Fermi liquid with
no residual degeneracy, or to a k-channel, spin-1/2 Kondo effect, or to a line
of ferromagnetic-like fixed points with a residual isospin-1/2 local moment.
These results are obtained through a combination of perturbative
renormalization-group techniques, Abelian bosonization, a strong-coupling
expansion in 1/J_z, and explicit numerical renormalization-group calculations.
