Abstract. Within the Hartree Fock- RPA analysis, we derive the spin wave spectrum for the weak ferromagnetic phase of the Hubbard model on the honeycomb lattice. Assuming a uniform magnetization, the polar (optical) and acoustic branches of the spin wave excitations are determined. The bipartite lattice geometry produces a q-dependent phase difference between the spin wave amplitudes on the two sub-lattices. We also find an instability of the uniform weakly magnetized configuration to a weak antiferromagnetic spiraling spin structure, in the lattice plane, with wave vector Q along the Γ − K direction, for electron densities n> 0.6. We discuss the effect of diagonal disorder on both the creation of electron bound states, enhancement of the density of states, and the possible relevance of these effects to disorder induced ferromagnetism, as observed in proton irradiated graphite
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