Abstract I will discuss the global phase diagram of the disordered Bose-Hubbard model in all dimensions controlled by the theorem of inclusions. In 1D, in the regime when strong disorder is more relevant than field quantization the superfluid--to--Bose-glass criticality is preceded by the prolonged logarithmically slow classical-field renormalization flow of the superfluid stiffness at mesoscopic scales. With the system compressibility remaining constant, the quantum nature of the system manifests itself only in the renormalization of dilute weak links. The transition point is still controlled by the proliferation of the instanton--anti-instanton pairs when the Luttinger liquid parameter equals 3/2, in accordance with the universal quantum scenario.
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