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Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J&#39; in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J&#39;. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.