  We analyse the distinction between the three different ground states
presented by a system of spinless bosons with short-range interactions
submitted to a random potential using the disordered Bose-Hubbard model. The
criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass
phases at finite temperatures are discussed for small values of the kinetic
energy associated with the tunnelling of particles between potential wells.
Field theoretical considerations are applied in order to construct a
diagrammatic hopping expansion to the finite-temperature Green's function. By
performing a summation of subsets of diagrams we are able to find the condition
to the long-range correlations which leads to the phase boundary between
superfluid and insulating phases. The perturbative expression to the local
correlations allows us to calculate an approximation to the single-particle
density of states of low-energy excitations in the presence of small hopping,
which characterizes unambiguously the distinction between the Mott-insulator
and the Bose-glass phases. We obtain the phase diagram for bounded on-site
disorder. It is demonstrated that our analysis is capable of going beyond the
mean-field theory results for the classification of these different ground
states.
