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The random antiferromagnetic two-leg and zigzag spin-1/2 ladders areinvestigated using the real space renormalization group scheme and theircomplete phase diagrams are determined. We demonstrate that the first systembelongs 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 weakfrustration and disorder. Otherwise, we give additional evidence that itbelongs to the universality class of the random antiferromagnetic andferromagnetic quantum spin chains, although the universal fixed point found inthe latter system is never realized. We find, however, a new universal fixedpoint at intermediate disorder.Comment: 10 pages, 10 figure

Phase diagrams and universality classes of random antiferromagnetic spin ladders