An investigation of the quantum J1-J2-J3 model on the honeycomb lattice

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