  We present an analytical theory for the magnetic phase diagram for zigzag
edge terminated honeycomb nanoribbons described by a Hubbard model with an
interaction parameter U . We show that the edge magnetic moment varies as ln U
and uncover its dependence on the width W of the ribbon. The physics of this
owes its origin to the sensory organ like response of the nanoribbons,
demonstrating that considerations beyond the usual Stoner-Landau theory are
necessary to understand the magnetism of these systems. A first order magnetic
transition from an anti-parallel orientation of the moments on opposite edges
to a parallel orientation occurs upon doping with holes or electrons. The
critical doping for this transition is shown to depend inversely on the width
of the ribbon. Using variational Monte-Carlo calculations, we show that
magnetism is robust to fluctuations. Additionally, we show that the magnetic
phase diagram is generic to zigzag edge terminated nanostructures such as
nanodots. Furthermore, we perform first principles modeling to show how such
magnetic transitions can be realized in substituted graphene nanoribbons.
