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.