An investigation of the quantum J(1)-J(2)-J(3) model on the honeycomb lattice

We have investigated the quantum J(1)-J(2)-J(3) model on the honeycomb latt ice with exact diag- onalizations and linear spin-wave calculations for sel ected values of J(2)/J(1) J(3)/J(1) and antiferromagnetic (J(1) > 0) or fer romagnetic (J(1) < 0) nearest neighbor interactions. We found a variety of quantum effects: "order by disorder" selection of a Neel ordered ground-sta te, good candidates for non-classical ground-states with dimer long range o rder or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be Neel ordered. Comparing these results with those observed o n tile square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models.