  We study the opening of the Haldane gap in two-leg and four-leg anisotropic
spin ladders using bosonization and renormalization group methods, and we
determine the phase diagram as a function of the interchain coupling and the
relative anisotropy. It is found that the opening of the Haldane gap is
qualitatively different for the two cases considered. For the two-leg ladder
the Haldane gap opens for arbitrarily small interchain coupling, independent of
the relative anisotropy, and the Haldane phase exists in a large region of
parameter space. For the four-leg ladder the opening of the Haldane gap is
strongly dependent on both the interchain coupling as well as the relative
anisotropy, and the Haldane phase exists only in a narrow region about the
isotropic antiferromagnet.
