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We study the ground state of the disordered Bose-Hubbard model for spin-1particles by means of the stochastic mean-field theory. This approach enablesthe determination of the probability distributions of various physicalquantities, such as the superfluid order parameter, the average site occupationnumber, the standard deviation of the occupation per site and the square of thespin operator per site. We show how a stochastic method, previously used in thestudy of localization, can be flexibly used to solve the relevant equationswith great accuracy. We have determined the phase diagram, which exhibits threephases: the polar superfluid, the Mott insulating and the Bose glass. Acomplete characterization of the physical properties of these phases has beenestablished.

Ground state properties of the disordered spin-one Bose-Hubbard model: a stochastic mean-field theory study