  The magnetism by the edge states in graphene is investigated theoretically.
An instability of the pseudo-spin order of the edge states induces
ferrimagnetic order in the presence of the Coulomb interaction. Although the
next nearest-neighbor hopping can stabilize the pseudo-spin order, a strong
Coulomb interaction makes the pseudo-spin unpolarized and real spin polarized.
The magnetism of the edge states makes two peaks of the density of states in
the conduction and valence energy bands near the Fermi point. Using a
continuous model of the Weyl equation, we show that the edge-induced gauge
field and the spin dependent mass terms are keys to make the magnetism of the
edge states. A relationship between the magnetism of the edge states and the
parity anomaly is discussed.
