Zero-temperature ordering in two-dimensional frustrated quantum Heisenberg antiferromagnets

We present series-expansion investigations of the square-lattice spin- (1/2 Heisenberg antiferromagnet with nearest-neighbor (J₁), second-neighbor (J₂), and third-neighbor (J₃) exchanges. Expansions for ground-state properties around dimerized Hamiltonians in conjunction with finite-size studies and cluster mean-field theories allow us to map out the magnetically ordered phase boundaries. The magnetically disordered phase of the square-lattice Heisenberg model, which is accessible to the dimer expansions, appears to be spontaneously dimerized in the ``columnar'' pattern predicted by Read and Sachdev. Estimates for the dimerization order parameter in this phase are a substantial fraction of that of the fully dimerized state.