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The one-dimensional isotropic quantum Heisenberg spin systems with randomcouplings and random spin sizes are investigated using a real-spacerenormalization group scheme. It is demonstrated that these systems belong to auniversality class of disordered spin systems, characterized by weakly coupledlarge effective spins. In this large-spin phase the uniform magneticsusceptibility diverges as 1/T with a non-universal Curie constant at lowtemperatures T, while the specific heat vanishes as T^delta |ln T| for T->0.For broad range of initial distributions of couplings and spin sizes thedistribution functions approach a single fixed-point form, where delta \approx0.44. For some singular initial distributions, however, fixed-pointdistributions have non-universal values of delta, suggesting that there is aline of fixed points.Comment: 19 pages, REVTeX, 13 figure

Low-energy fixed points of random quantum spin chains