  Using the density matrix renormalization group (DMRG) on wide cylinders, we
study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with
first-neighbor ($J_1 = 1$) and frustrating second-neighbor ($J_2>0$)
interactions. For the intermediate frustration regime $0.22\lesssim
J_2\lesssim0.36$, we find a surprising antiferromagnetic Ising phase, with
ordered moments pointing along the z axis, despite the absence of any S_z_z
interactions in the Hamiltonian. Surrounding this phase as a function of $J_2$
are antiferromagnetic phases with the moments pointing in the $x-y$ plane for
small $J_2$ and a close competition between an $x-y$ plane magnetic collinear
phase and a dimer phase for large values of $J_2$. We do not find any spin
liquid phases in this model.
