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We study magnetically ordered phases and their phase boundaries in the$J_1-J_2-J_3$ Heisenberg models on the honeycomb lattice using seriesexpansions around N\'eel and different colinear and non-colinear magneticstates. An Ising anisotropy ($\lambda=J_{\perp}/J_z\ne 1$) is introduced andground state energy and magnetization order parameter are calculated as a powerseies expansion in $\lambda$. Series extrapolation methods are used to studyproperties for the Heisenberg model ($\lambda=1$). We find that at large $J_3$($>0.6$) there is a first order transition between N\'eel and columnar states,in agreement with the classical answer. For $J_3=0$, we find that the N\'eelphase extends beyond the region of classical stability. We also find thatspiral phases are stabilized over large parameter regions, although theirspiral angles can be substantially renormalized with respect to the classicalvalues. Our study also shows a magnetically disordered region at intermedaite$J_2/J_1$ and $J_3/J_1$ values.

Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study