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We have studied the spectrum of low-spin eigenstates of a spin- (1/2 Heisenberg model on 44 square lattices with up to third-neighbor antiferromagnetic exchange interactions. We have computed the staggered susceptibility, spin-spin correlation function, and the overlap of the exact ground state with various variational spin-density-wave ordered states as well as with the equal-amplitude, nearest-neighbor resonating-valence-bond state (which is the prototypical short-ranged RVB state). We find evidence for a complicated phase diagram with a region in which a short-ranged RVB state may be the ground state.
Figueirido et al. (Thu,) studied this question.