We use series expansions around the Ising limit to study several anisotropic quantum spin models on the honeycomb and triangular lattices. These include the antiferromagnetic spin-1/2 and spin-1 Heisenberg model, and the XY antiferromagnet on the honeycomb lattice, and also the XY ferromagnet on the triangular lattice. Series are calculated for the ground-state energy, energy gap, magnetization, and magnetic susceptibility in each spin direction. Extrapolating these series to the isotropic limit, we find quite good agreement with the predictions of spin-wave theory.

• Received 6 November 1991

DOI:https://doi.org/10.1103/PhysRevB.45.9834