  We investigate the effect of weak randomness on the antiferromagnetic
anisotropic spin-1 chain. We use Abelian bosonization to construct the
low-energy effective theory. A renormalization group calculation up to second
order in the strength of the disorder is performed on this effective theory. We
observe in this framework the destruction of the antiferromagnetic ordered
phase `a la Imry-Ma. We predict the effects of a random magnetic field along z
axis, a random field in the XY plane as well as random exchange with and
without XY symmetry. Instabilities of massless phases appear in general by
mechanisms different from the case of the 2-leg spin ladder.

Statistical Mechanics;Disordered Systems and Neural Networks