Quantum phase transitions in a large class of one-dimensional and some
higher-dimensional quantum magnets with quenched disorder are
described by an infinite randomness fixed point. Unusual scaling laws
and the occurence of Griffiths-McCoy singularities away from the
critical point characterize theses universality classes, which have
been studied with a strong disorder renormalization group (SDRG),
exact diagonalization and quantum Mone-Carlo methods. A coupling of
the spin degrees of freedom to a dissipative bosonic bath alters this
scenario significantly: The sharp quantum phase transition is smeared
and the Griffiths-McCoy singularities become dominated by a classical
behavior of the susceptibility and specific heat below a crossover
temperature T*. By combining the SDRG with a renormalization scheme for
the spin-boson-system it became possible to describe this crossover
quantitatively in random transverse field Ising systems and possibly
also in other quantum spin systems.