Possible crossover to percolation scenario near superfluid-Bose-glass transition

Abstract We discuss magnetically ordered (“superfluid”) phase near quantum transition to Bose-glass phase in a simple modeling system, Heisenberg antiferromagnet in spatial dimension d > 2 in external magnetic field with disorder in exchange coupling constants. Our analytical consideration is based on hydrodynamic description of long-wavelength excitations and it is valid in the entire critical region near the quantum critical point (QCP). We demonstrate that the system behaves in full agreement with predictions by Fisher et al. (Phys. Rev. B 40, 546 (1989)) in close vicinity of QCP. On the other hand, we show that many recent experimental and numerical results obtained in various 3D systems can be described by our formulas using percolation critical exponents. Then, it is a possibility that a percolation critical regime arises in the ordered phase in some 3D systems not very close to QCP.