By the example of Heisenberg d-dimensional disordered antiferromagnets, we discuss quantum transitions at d ≥ 2 from magnetically ordered (superfluid) to various disordered (insulating) glassy phases (Bose-glass, Mott-glass, etc.) in Bose systems with quenched disorder. Our consideration is based on the hydrodynamic description of long-wavelength excitations and on the assumption that the ordered part of the system shows fractal properties near the transition point. We propose that the scaling ansatz for the free energy suggested before for the transition to the Bose-glass phase is applicable also for other transitions if the quenched disorder does not produce a local imbalance in sublattices magnetizations. We show using the scaling consideration that η = 2 − z and β = νd/2, where η, β, and ν, are critical exponents of the correlation function, the order parameter, and the correlation length, respectively, and z is the dynamical critical index. These relations were missed in previous analytical discussions of Bose-glass and Mott-glass phases. They signify, in particular, that z = d/2 for the transition to the Mott-glass phase and that the density of states of localized excitations shows a superuniversal (i.e., independent of d) behavior near the transitions. Being derived solely from the scaling analysis, the above relations for η and β are valid also for the transition to the random-singlet phase.
We discuss theoretically the magnetically ordered phase induced by magnetic and nonmagnetic impurities in three-dimensional and quasi-low-dimensional systems with singlet ground states separated by a gap from the excited triplet states. Using ideas of the percolation theory, we estimate the transition temperature TN (n) to the Néel phase and derive the density of states of low-energy elementary excitations at a small concentration n of defects. Our expression for TN (n) describes well available experimental findings obtained in various appropriate systems: spin-1 2 dimer materials, spin-ladder compounds, spin-Peierls and Haldane chain materials. However, our expression for TN (n) differs considerably from those proposed before.
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