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We study the effects of dissipation on a randomly diluted transverse-fieldIsing magnet close to the percolation threshold. For weak transverse fields, anovel percolation quantum phase transition separates a superparamagneticcluster phase from an inhomogeneously ordered ferromagnetic phase. Theproperties of this transition are dominated by large frozen and slowlyfluctuating percolation clusters. This leads to a discontinuousmagnetization-field curve and exotic hysteresis phenomena as well as highlysingular behavior of magnetic susceptibility and specific heat. We compare ourresults to the smeared transition in generic dissipative random quantum Isingmagnets. We also discuss the relation to metallic quantum magnets and otherexperimental realizations.Comment: 4 pages, 2 eps figures, final version as publishe

Percolation transition and dissipation in quantum Ising magnets