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The two-dimensional frustrated next nearest neighbor Heisenberg model on thesquare lattice is a prime example for a spin system where quantum fluctuationscan either destroy or stabilize magnetic order. The phase boundaries andstaggered moment dependence on the frustration ratio J_2/J_1 of the exchangeconstants are fairly well understood both from approximate analytical andnumerical methods. In this work we use exact diagonalization for finiteclusters for an extensive investigation of the more general J_1a,b-J_2 modelwhich includes a spatial exchange anisotropy between next-neighbor spins. Weintroduce a systematic way of tiling the square lattice and, for this lowsymmetry model, define a controlled procedure for the finite size scaling thatis compatible with the possible magnetic phases. We obtain ground stateenergies, structure factors and ordered moments and compare with the results ofspin wave calculations. We conclude that J_1a,b exchange anisotropy stronglystabilizes the columnar antiferromagnetic phase for all frustration parameters,in particular in the region of the spin nematic phase of the isotropic model.

Ordered moment in the anisotropic and frustrated square lattice Heisenberg model