  In the present paper we discuss the rich phase diagram of S=1/2 weakly
coupled dimer systems with site dilution as a function of an applied uniform
magnetic field. Performing quantum Monte Carlo simulations on a site-diluted
bilayer system, we find a sequence of three distinct quantum-disordered phases
induced by the field. Such phases divide a doping-induced order-by-disorder
phase at low fields from a field-induced ordered phase at intermediate fields.
The three quantum disordered phases are: a gapless disordered-free-moment
phase, a gapped plateau phase, and two gapless Bose-glass phases. Each of the
quantum-disordered phases have distinct experimental signatures that make them
observable through magnetometry and neutron scattering measurements. In
particular the Bose-glass phase is characterized by an unconventional
magnetization curve whose field-dependence is exponential. Making use of a
local-gap model, we directly relate this behavior to the statistics of rare
events in the system.
