  The effect of quenched disorder on the low-energy properties of various
antiferromagnetic spin ladder models is studied by a numerical strong disorder
renormalization group method and by density matrix renormalization. For strong
enough disorder the originally gapped phases with finite topological or dimer
order become gapless. In these quantum Griffiths phases the scaling of the
energy, as well as the singularities in the dynamical quantities are
characterized by a finite dynamical exponent, z, which varies with the strength
of disorder. At the phase boundaries, separating topologically distinct
Griffiths phases the singular behavior of the disordered ladders is generally
controlled by an infinite randomness fixed point.
