We use a large-N renormalization-group (RG) method to study a model of interacting boson system with a quenched random potential. In the absence of impurities, the pure boson system has a critical point that describes the superfluid–Mott-insulator (SF–MI) transition. The SF–MI transition of d-dimensional bosons belongs to the (d+1)-dimensional XY model universality class. In this paper, we study the dirty-boson critical points in the neighborhood of this pure SF–MI critical point. In general, the on-site random potential in the original lattice model gives two types of randomness in the effective-field-theoretic action. One is the randomness in the effective on-site repulsion w(x) and the other is the randomness of the chemical potential u(x). It turns out that d=2 is the critical dimension for both types of disorder but the roles of these two types of disorder are reversed as d=2 is crossed. Applying ε=d-2 expansion, we found coupled RG equations for both kinds of randomness which reveal several nontrivial critical points. All the weak random fixed points we found have three or more relevant directions. We conclude that the direct SF–MI transition is unlikely to occur near two dimensions.

• Received 30 August 1993

DOI:https://doi.org/10.1103/PhysRevB.49.4043