  We study the effects of dissipation on a randomly dilute transverse-field
Ising magnet at and close to the percolation threshold. For weak transverse
fields, a novel percolation quantum phase transition separates a
super-paramagnetic cluster phase from an inhomogeneously ordered ferromagnetic
phase. The properties of this transition are dominated by large frozen and
slowly fluctuating percolation clusters. Implementing numerically a
strong-disorder real space renormalization group technique, we compute the
low-energy density of states which is found to be in good agreement with the
analytical prediction.
