Disorder induced cross-over effects at quantum critical points.

Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system, and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent.