  Random spin-3/2 antiferromagnetic Heisenberg chains are investigated using an
asymptotically exact renormalization group. Randomness is found to induce a
quantum phase transition between two random-singlet phases. In the strong
randomness phase the effective spins at low energies are S_eff=3/2, while in
the weak randomness phase the effective spins are S_eff=1/2. Separating them is
a quantum critical point near which there is a non-trivial mixture of S=1/2,
S=1, and S=3/2 effective spins at low temperatures.
