  We study the effects of disorder in two-dimensional quantum antiferromagnets
on a square lattice, within the nonlinear sigma model approach, by using of a
random 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. The large distance behavior of the quenched spin correlation
function 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 disorder state. A comparison is made with the dual behavior
of skyrmion topological excitations in the renormalized classical phase.
