Low-energy fixed points of random Heisenberg models

The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization-group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, ω, describing the low-energy tail of the gap distribution P(Δ)∼Δ ω is independent of disorder, the strength of couplings, and the value of the spin. The dynamical behavior of nonfrustrated random antiferromagnetic models is controlled by a singletlike fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent is given by ω0. Another type of universality class is observed at quantum critical points and in dimerized phases but no infinite randomness behavior is found, in contrast to that of one-dimensional models.