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

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