  We examine phases of the Shraiman-Siggia model of lightly-doped, square
lattice quantum antiferromagnets in a self-consistent, two-loop, interacting
magnon analysis. We find magnetically-ordered and quantum-disordered phases
both with and without incommensurate spin correlations. The quantum disordered
phases have a pseudo-gap in the spin excitation spectrum. The quantum
transition between the magnetically ordered and commensurate quantum-disordered
phases is argued to have the dynamic critical exponent $z=1$ and the same
leading critical behavior as the disordering transition in the pure $O(3)$
sigma model. The relationship to experiments on the doped cuprates is
discussed.
