Mean-field phase diagram of disordered bosons in a lattice at nonzero temperature

Bosons in a periodic lattice with on-site disorder at low but nonzero temperatures are considered within a mean-field theory. The criteria used for the definition of the superfluid, Mott insulator and Bose glass are analysed. Since the compressibility never vanishes at nonzero temperatures, it cannot be used as a general criterion. We show that the phases are unambiguously distinguished by the superfluid density and the density of states of the low-energy excitations. The phase diagram of the system is calculated. It is shown that even a tiny temperature leads to a significant shift of the boundary between the Bose glass and superfluid.