Random spin-$\frac{3}{2}$ 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 $S_{\mathrm{eff}}=\frac{3}{2},$ while in the weak randomness phase the effective spins are $S_{\mathrm{eff}}=\frac{1}{2}.$ Separating them is a quantum critical point near which there is a nontrivial mixture of spin-$\frac{1}{2},$ spin-$1,$ and spin-$\frac{3}{2}$ effective spins at low temperatures.

• Received 6 June 2002

DOI:https://doi.org/10.1103/PhysRevB.66.060402