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We study the insulator-to-superfluid transition in a two-dimensionaldisordered boson Hubbard model at zero temperature for intermediate strength ofdisorder at commensurate density. Via Monte Carlo calculations of thecorrelation functions in the integer current representation of the model, weobtain the dynamical critical exponent $z=1.5 \pm 0.1$, supporting themulti-critical behavior separating the strong and weak disorder regimes.Investigating the density profile, we suggest that the density fluctuations dueto the particle-hole excitations drive the transition in the weak disorderregime.Comment: to be published in PR

Separation of two regimes in a disordered boson Hubbard model