Effects of disorder in two-dimensional quantum antiferromagnets

We study the effects of disorder in two-dimensional quantum antiferromagnets on a square lattice, within the nonlinear sigma model approach, by using a random continuum distribution of spin stiffnesses or zero-temperature spin gaps, respectively, in the renormalized classical and quantum disordered phases. The quenched staggered magnetic susceptibility at low temperatures is evaluated in each case, showing that the phase structure of the clean system is preserved. The asymptotic behavior of the quenched static and dynamic spin correlation functions is also obtained in the quantum disordered phase. Disorder is shown to introduce a change from exponential to power-law decay in these functions, indicating that the spin excitations become gapless, in spite of the fact that the system is in a paramagnetic state. The scale determining the change in behavior is related to the variance of the distribution function. A comparison is made with the dual behavior of skyrmion topological excitations in the renormalized classical phase. The effect found here is compared with the one produced by Griffiths singularities occurring in disordered systems.