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The effect of quenched disorder on the low-energy and low-temperatureproperties of various two- and three-dimensional Heisenberg models is studiedby a numerical strong disorder renormalization group method. For strong enoughdisorder we have identified two relevant fixed points, in which the gapexponent, omega, describing the low-energy tail of the gap distribution,P(Delta) ~ Delta^omega is independent of disorder, the strength of couplingsand the value of the spin. The dynamical behavior of non-frustrated randomantiferromagnetic models is controlled by a singlet-like fixed point, whereasfor frustrated models the fixed point corresponds to a large spin formation andthe gap exponent is given by omega ~ 0. Another type of universality classes isobserved at quantum critical points and in dimerized phases but no infiniterandomness behavior is found, in contrast to one-dimensional models.Comment: 11 pages RevTeX, eps-figs included, language revise

Low-energy fixed points of random Heisenberg models