  Effects of randomness on the spin-1/2 and 1 antiferromagnetic Heisenberg
chains are studied using the quantum Monte Carlo method with the
continuous-time loop algorithm. We precisely calculated the uniform
susceptibility, string order parameter, spatial and temporal correlation
length, and the dynamical exponent, and obtained a phase diagram. The
generalization of the continuous-time loop algorithm for the systems with
higher-S spins is also presented.
