The random antiferromagnetic two-leg and zigzag spin-1/2 ladders are
investigated using the real space renormalization group scheme and their
complete phase diagrams are determined. We demonstrate that the first system
belongs to the same universality class of the dimerized random spin-1/2 chain.
The zigzag ladder, on the other hand, is in a random singlet phase at weak
frustration and disorder. Otherwise, we give additional evidence that it
belongs to the universality class of the random antiferromagnetic and
ferromagnetic quantum spin chains, although the universal fixed point found in
the latter system is never realized. We find, however, a new universal fixed
point at intermediate disorder.Comment: 10 pages, 10 figure